Two Variable Systems of Linear Equations

Multiple Choice

Use substitution to solve the following system of linear equations.

$4x+y=1$

$x-y=4$

Use substitution to solve the following system of linear equations.

$4x+2y=7$

$x+5y=4$

Use the elimination method to solve the following system of linear equations.

$2x+y=1$

$3x-y=4$

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Multiple Choice

Use the elimination method to solve the following system of linear equations.

$10x-4y=5$

$5x-4y=1$

Solve the following system of equations. Classify it as CONSISTENT (INDEPENDENT or DEPENDENT) or INCONSISTENT.

$y=5x-17$

$15x-3y=51$

Solve the following system of equations. Classify it as CONSISTENT (INDEPENDENT or DEPENDENT) or INCONSISTENT.

$2x+8y=7$

$x+4y=19$

Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions, write the solution set with y arbitrary. 2x + 6y = 6 5x + 9y = 9

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Textbook Question

In Exercises 1–4, determine whether the given ordered pair is a solution of the system. (2, 3) x + 3y = 11 x - 5y = - 13

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Textbook Question

In Exercises 1–5, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets.

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Textbook Question

In Exercises 1–4, determine whether the given ordered pair is a solution of the system. (- 3, 5) 9x + 7y = 8 8x - 9y = - 69

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Textbook Question

In Exercises 1–5, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets.

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Textbook Question

In Exercises 1–5, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets.

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Textbook Question

In Exercises 1–4, determine whether the given ordered pair is a solution of the system. (2, 5) 2x + 3y = 17 x + 4y = 16

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Textbook Question

Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions, write the solution set with y arbitrary. 1/6x + 1/3y = 8 1/4x + 1/2y = 12

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Textbook Question

In Exercises 5–18, solve each system by the substitution method. x + y = 4 y = 3x

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Textbook Question

A chemist needs to mix a solution that is 34% silver nitrate with one that is 4% silver nitrate to obtain 100 milliliters of a mixture that is 7% silver nitrate. How many milliliters of each of the solutions must be used?

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Textbook Question

In Exercises 5–18, solve each system by the substitution method. x + 3y = 8 y = 2x - 9

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Textbook Question

Solve each system by substitution. See Example 1. 4x + 3y = -13 -x + y = 5

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Textbook Question

A chemist needs to mix a solution that is 34% silver nitrate with one that is 4% silver nitrate to obtain 100 milliliters of a mixture that is 7% silver nitrate. How many milliliters of each of the solutions must be used?

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Textbook Question

Solve each system by substitution. See Example 1. x - 5y = 8 x = 6y

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Textbook Question

The perimeter of a table tennis top is 28 feet. The difference between 4 times the length and 3 times the width is 21 feet. Find the dimensions.

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Textbook Question

In Exercises 5–18, solve each system by the substitution method. x = 4y - 2 x = 6y + 8

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Textbook Question

Solve each problem. Alcohol MixtureBarak wishes to strengthen a mixture that is 10% alcohol to onethat is 30% alcohol. How much pure alcohol should he add to 12 L of the 10% mixture?

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Textbook Question

In Exercises 5–18, solve each system by the substitution method. 5x + 2y = 0 x - 3y = 0

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Textbook Question

In Exercises 5–18, solve each system by the substitution method. 5x + 2y = 0 x - 3y = 0

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Textbook Question

In Exercises 5–18, solve each system by the substitution method. 2x + 5y = - 4 3x - y = 11

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Textbook Question

Solve each system by substitution. See Example 1. 7x - y = -10 3y - x = 10

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Textbook Question

In Exercises 5–18, solve each system by the substitution method. 2x - 3y = 8 - 2x 3x + 4y = x + 3y + 14

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Textbook Question

Solve each system by substitution. See Example 1. -2x = 6y + 18 -29 = 5y - 3x

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Textbook Question

Solve each problem using a system of equations. A company sells recordable CDs for $0.80 each and play-only CDs for $0.60 each. The company receives $76.00 for an order of 100 CDs. However, the customer neglected to specify how many of each type to send. Determine the number of each type of CD that should be sent.

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Textbook Question

In Exercises 5–18, solve each system by the substitution method. y = (1/3)x + 2/3 y = (5/7)x - 2

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Textbook Question

Solve each system by substitution. See Example 1. 3y = 5x + 6 x + y = 2

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Textbook Question

Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2. 4x + y = -23 x - 2y = -17

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Textbook Question

In Exercises 19–30, solve each system by the addition method. x + y = 1 x - y = 3

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Textbook Question

In Exercises 19–30, solve each system by the addition method. 2x + 3y = 6 2x - 3y = 6

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Textbook Question

In Exercises 19–30, solve each system by the addition method. 2x + 3y = 6 2x - 3y = 6

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Textbook Question

In Exercises 19–30, solve each system by the addition method. x + 2y = 2 - 4x + 3y = 25

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Textbook Question

Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2. 5x + 7y = 6 10x - 3y = 46

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Textbook Question

In Exercises 19–30, solve each system by the addition method. 4x + 3y = 15 2x - 5y = 1

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Textbook Question

Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2. 6x + 7y + 2 = 0 7x - 6y - 26 = 0

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Textbook Question

In Exercises 19–30, solve each system by the addition method. 3x - 4y = 11 2x + 3y = - 4

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Textbook Question

Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2. x/2+ y/3 = 4 3x/2+3y/2 = 15

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Textbook Question

Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2. (2x-1)/3 + (y+2)/4 = 4 (x+3)/2 - (x-y)/2 = 3

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Textbook Question

In Exercises 19–30, solve each system by the addition method. 3x = 4y + 1 3y = 1 - 4x

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Textbook Question

In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. x = 9-2y x + 2y = 13

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Textbook Question

Solve each system of equations. State whether it is an inconsistent system or has infinitely many solutions. If a system has infinitely many solutions, write the solution set with x arbitrary. See Examples 3 and 4. 9x - 5y = 1 -18x + 10y = 1

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Textbook Question

In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. y = 3x - 5 21x - 35 = 7y

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Textbook Question

In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. 3x - 2y = − 5 4x + y = 8

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Textbook Question

Solve each system of equations. State whether it is an inconsistent system or has infinitely many solutions. If a system has infinitely many solutions, write the solution set with x arbitrary. See Examples 3 and 4. 5x - 5y - 3 = 0 x - y - 12 = 0

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Textbook Question

In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. x + 3y = 2 3x + 9y = 6

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Textbook Question

In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. x + 3y = 2 3x + 9y = 6

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Textbook Question

In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. x/4 - y/4 = −1 x + 4y = -9

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Textbook Question

In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. 2x = 3y + 4 4x = 3 - 5y

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Textbook Question

Determine the system of equations illustrated in each graph. Write equations in standard form.

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Textbook Question

Determine the system of equations illustrated in each graph. Write equations in standard form.

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Textbook Question

In Exercises 43–46, let x represent one number and let y represent the other number. Use the given conditions to write a system of equations. Solve the system and find the numbers. The sum of two numbers is 7. If one number is subtracted from the other, their difference is -1. Find the numbers.

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Textbook Question

In Exercises 47–48, solve each system by the method of your choice. (x + 2)/2 - (y + 4)/3 = 3 (x + y)/5 = (x - y)/2 - 5/2

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Textbook Question

In Exercises 47–48, solve each system by the method of your choice. (x - y)/3 = (x + y)/2 - 1/2 (x + 2)/2 - 4 = (y + 4)/3

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Textbook Question

In Exercises 47–48, solve each system by the method of your choice. (x - y)/3 = (x + y)/2 - 1/2 (x + 2)/2 - 4 = (y + 4)/3

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Textbook Question

In Exercises 49–50, solve each system for x and y, expressing either value in terms of a or b, if necessary. Assume that a ≠ 0, b ≠ 0 5ax + 4y = 17 ax + 7y = 22

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Textbook Question

Solve each system. (Hint: In Exercises 69–72, let 1/x = t and 1/y = u.) 2/x + 3/y = 18 4/x - 5/y = -8

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Textbook Question

Use a system of linear equations to solve Exercises 73–84. How many ounces of a 15% alcohol solution must be mixed with 4 ounces of a 20% alcohol solution to make a 17% alcohol solution?

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Textbook Question

For what value(s) of k will the following system of linear equations have no solution? infinitely many solutions? x - 2y = 3 -2x + 4y = k

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Textbook Question

Use a system of linear equations to solve Exercises 73–84. How many ounces of a 50% alcohol solution must be mixed with 80 ounces of a 20% alcohol solution to make a 40% alcohol solution?

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Textbook Question

Use a system of equations to solve each problem. See Example 8. Find an equation of the line y = ax + b that passes through the points (-2, 1) and (-1, -2).

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Textbook Question

Use a system of equations to solve each problem. See Example 8. Find an equation of the parabola y = ax^2 + bx + c that passes through the points (2, 3), (-1, 0), and (-2, 2).

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Textbook Question

Exercises 86–88 will help you prepare for the material covered in the first section of the next chapter. a. Does (4, −1) satisfy x + 2y = 2? b. Does (4, -1) satisfy x- 2y= 6?

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Textbook Question

Exercises 86–88 will help you prepare for the material covered in the first section of the next chapter. a. Does (4, −1) satisfy x + 2y = 2? b. Does (4, -1) satisfy x- 2y= 6?

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Textbook Question

Solve each problem. See Examples 5 and 9. The sum of two numbers is 47, and the difference between the numbers is 1. Find the numbers.

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