7. Systems of Equations & Matrices

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

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 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.

-2x = 6y + 18

-29 = 5y - 3x

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

In Exercises 29–42, solve each system by the method of your choice. $\(\begin{cases}\)2x^2 + y^2 = 18 \\(\xy\) = 4\(\end{cases}\)$

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

Solve each problem using a system of equations in two variables. See Example 6. Find two numbers whose ratio is 9 to 2 and whose product is 162.

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?

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.

6x + 10y = -11

9x + 6y = -3

In Exercises 1–18, solve each system by the substitution method. $\(\begin{cases}\)x + y = 1 \\(\x\)^2 + xy - y^2 = -5\(\end{cases}\)$

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).

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?

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.

In Exercises 29–42, solve each system by the method of your choice. $\(\begin{cases}\)x^3 + y = 0 \\(\x\)^2 - y = 0\(\end{cases}\)$