7. Systems of Equations & Matrices

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 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.

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

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

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

Solve each system. (Hint: In Exercises 69–72, let $1/x=t$ and $1/y=u$.)

$\frac{2}{x}+\frac{3}{y}=18$

$\frac{4}{x}-\frac{5}{y}=-8$

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?

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

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?

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).

Use a system of equations to solve each problem. Find an equation of the parabola y = ax² + bx + c that passes through the points (2, 3), (-1, 0), and (-2, 2).

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?

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.

Solve the system