7. Systems of Equations & Matrices

Solve each system by elimination. In systems with fractions, first clear denominators.

(2x-1)/3 + (y+2)/4 = 4

(x+3)/2 - (x-y)/2 = 3

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?

Use substitution to solve the following system of linear equations.

$4x+2y=7$

$x+5y=4$

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?

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

Solve each problem. The supply and demand equations for a certain commodity are given. supply: p = 2000/(2000 - q) and demand: p = (7000 - 3q)/2q.

Find the equilibrium price (in dollars).

In Exercises 25–35, solve each system by the method of your choice. This is a piecewise function, refer to textbook problem.

Solve each problem. Find the radius and height (to the nearest thousandth) of an open-ended cylinder with volume 50 in.³ and lateral surface area 65 in.².

Solve each system by elimination. In systems with fractions, first clear denominators.

x/2+ y/3 = 4

3x/2+3y/2 = 15

Solve each problem. The supply and demand equations for a certain commodity are given. supply: p = √(0.1q + 9) - 2 and demand: p = √(25 - 0.1q).

Find the equilibrium demand.

In Exercises 19–28, solve each system by the addition method. $\(\begin{cases}\)3x^2 + 4y^2 - 16 = 0 \\2x^2 - 3y^2 - 5 = 0\(\end{cases}\)$

Solve each system by elimination. In systems with fractions, first clear denominators.

6x + 7y + 2 = 0

7x - 6y - 26 = 0

Solve each system by substitution.

3y = 5x + 6

x + y = 2

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components.

x² - y = 0

x + y = 2

In Exercises 19–28, solve each system by the addition method. $\(\begin{cases}\)x^2 - 4y^2 = -7 \\3x^2 + y^2 = 31\(\end{cases}\)$