7. Systems of Equations & Matrices

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 = 17ax + 7y = 22

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 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. 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).

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

Solve the systems in Exercises 79–80. log x^2=y+3, log x=y−1

Solve the systems in Exercises 79–80. log_y x=3, log_y (4x)=5

Find the length and width of a rectangle whose perimeter is 40 feet and whose area is 96 square feet.

Find the length and width of a rectangle whose perimeter is 36 feet and whose area is 77 square feet.