# Two Variable Systems of Linear Equations - Video Tutorials & Practice Problems

## Introduction to Systems of Linear Equations

## Example 1

## Example 2

## Solving Systems of Equations - Substitution

Use substitution to solve the following system of linear equations.

$4x+y=1$

$x-y=4$

$\left(-1,3\right)$

$\left(-3,1\right)$

$\left(3,-1\right)$

$\left(1,-3\right)$

Use substitution to solve the following system of linear equations**.**

$4x+2y=7$

$x+5y=4$

$\left(\frac12,\frac32\right)$

$\left(\frac32,\frac12\right)$

$\left(-\frac23,\frac13\right)$

$\left(-\frac13,\frac23\right)$

## Solving Systems of Equations - Elimination

## How to Multiply Equations in Elimination Method

## Example 3

## Example 4

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

$2x+y=1$

$3x-y=4$

$\left(-1,1\right)$

$\left(1,1\right)$

$\left(1,-1\right)$

$\left(-1,-1\right)$

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

$10x-4y=5$

$5x-4y=1$

$x=12,y=16$

$x=16,y=12$

$x=\frac34,y=\frac45$

$x=\frac45,y=\frac34$

## Classifying Systems of Linear Equations

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

$y=5x-17$

$15x-3y=51$

Consistent and Independent

Consistent and Dependent

Inconsistent

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

$2x+8y=7$

$x+4y=19$

Consistent and Independent

Consistent and Dependent

Inconsistent

## Do you want more practice?

- Use the substitution or elimination method to solve each system of equations. Identify any inconsistent system...
- In Exercises 1–4, determine whether the given ordered pair is a solution of the system. (2, 3) x + 3y = 11 x...
- In Exercises 1–5, solve by the method of your choice. Identify systems with no solution and systems with infin...
- In Exercises 1–4, determine whether the given ordered pair is a solution of the system. (- 3, 5) 9x + 7y = 8...
- In Exercises 1–5, solve by the method of your choice. Identify systems with no solution and systems with infin...
- In Exercises 1–5, solve by the method of your choice. Identify systems with no solution and systems with infin...
- In Exercises 1–4, determine whether the given ordered pair is a solution of the system. (2, 5) 2x + 3y = 17 x...
- Use the substitution or elimination method to solve each system of equations. Identify any inconsistent system...
- In Exercises 5–18, solve each system by the substitution method. x + y = 4 y = 3x
- A chemist needs to mix a solution that is 34% silver nitrate with one that is 4% silver nitrate to obtain 100 ...
- In Exercises 5–18, solve each system by the substitution method. x + 3y = 8 y = 2x - 9
- Solve each system by substitution. See Example 1. 4x + 3y = -13 -x + y = 5
- A chemist needs to mix a solution that is 34% silver nitrate with one that is 4% silver nitrate to obtain 100 ...
- Solve each system by substitution. See Example 1. x - 5y = 8 x = 6y
- The perimeter of a table tennis top is 28 feet. The difference between 4 times the length and 3 times the widt...
- In Exercises 5–18, solve each system by the substitution method. x = 4y - 2 x = 6y + 8
- Solve each problem. Alcohol MixtureBarak wishes to strengthen a mixture that is 10% alcohol to onethat is 30% ...
- In Exercises 5–18, solve each system by the substitution method. 5x + 2y = 0 x - 3y = 0
- In Exercises 5–18, solve each system by the substitution method. 5x + 2y = 0 x - 3y = 0
- In Exercises 5–18, solve each system by the substitution method. 2x + 5y = - 4 3x - y = 11
- Solve each system by substitution. See Example 1. 7x - y = -10 3y - x = 10
- In Exercises 5–18, solve each system by the substitution method. 2x - 3y = 8 - 2x 3x + 4y = x + 3y + 14
- Solve each system by substitution. See Example 1. -2x = 6y + 18 -29 = 5y - 3x
- Solve each problem using a system of equations. A company sells recordable CDs for $0.80 each and play-only CD...
- In Exercises 5–18, solve each system by the substitution method. y = (1/3)x + 2/3 y = (5/7)x - 2
- Solve each system by substitution. See Example 1. 3y = 5x + 6 x + y = 2
- Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2. 4x + y =...
- In Exercises 19–30, solve each system by the addition method. x + y = 1 x - y = 3
- In Exercises 19–30, solve each system by the addition method. 2x + 3y = 6 2x - 3y = 6
- In Exercises 19–30, solve each system by the addition method. 2x + 3y = 6 2x - 3y = 6
- In Exercises 19–30, solve each system by the addition method. x + 2y = 2 - 4x + 3y = 25
- Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2. 5x + 7y ...
- In Exercises 19–30, solve each system by the addition method. 4x + 3y = 15 2x - 5y = 1
- Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2. 6x + 7y ...
- In Exercises 19–30, solve each system by the addition method. 3x - 4y = 11 2x + 3y = - 4
- Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2. x/2+ y/3...
- Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2. (2x-1)/3...
- In Exercises 19–30, solve each system by the addition method. 3x = 4y + 1 3y = 1 - 4x
- In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with inf...
- Solve each system of equations. State whether it is an inconsistent system or has infinitely many solutions. I...
- In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with inf...
- In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with inf...
- Solve each system of equations. State whether it is an inconsistent system or has infinitely many solutions. I...
- Determine the system of equations illustrated in each graph. Write equations in standard form.
- Determine the system of equations illustrated in each graph. Write equations in standard form.
- In Exercises 43–46, let x represent one number and let y represent the other number. Use the given conditions ...
- In Exercises 47–48, solve each system by the method of your choice. (x + 2)/2 - (y + 4)/3 = 3 (x + y)/5 = (x...
- In Exercises 47–48, solve each system by the method of your choice. (x - y)/3 = (x + y)/2 - 1/2 (x + 2)/2 - ...
- In Exercises 47–48, solve each system by the method of your choice. (x - y)/3 = (x + y)/2 - 1/2 (x + 2)/2 - ...
- In Exercises 49–50, solve each system for x and y, expressing either value in terms of a or b, if necessary. A...
- 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
- Use a system of linear equations to solve Exercises 73–84. How many ounces of a 15% alcohol solution must be m...
- For what value(s) of k will the following system of linear equations have no solution? infinitely many solutio...
- Use a system of linear equations to solve Exercises 73–84. How many ounces of a 50% alcohol solution must be m...
- Use a system of equations to solve each problem. See Example 8. Find an equation of the line y = ax + b that p...
- Use a system of equations to solve each problem. See Example 8. Find an equation of the parabola y = ax^2 + bx...
- Exercises 86–88 will help you prepare for the material covered in the first section of the next chapter. a. Do...
- Exercises 86–88 will help you prepare for the material covered in the first section of the next chapter. a. Do...
- Solve each problem. See Examples 5 and 9. The sum of two numbers is 47, and the difference between the numbers...