7. Systems of Equations & Matrices

In Exercises 1–4, determine whether the given ordered pair is a solution of the system. (2, 5) 2x + 3y = 17 x + 4y = 16

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.

$\frac{1}{6x}+\frac{1}{3y}=8$

$\frac{1}{4x}+\frac{1}{2y}=12$

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 milliliters of a mixture that is 7% silver nitrate. How many milliliters of each of the solutions must be used?

In Exercises 5–18, solve each system by the substitution method. $\begin{cases}x + 3y = 8 \\y = 2x - 9\end{cases}$

Solve each system by substitution.

4x + 3y = -13

-x + y = 5

Solve each system by substitution.

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 width is 21 feet. Find the dimensions.

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In Exercises 5–18, solve each system by the substitution method. $\begin{cases}x = 4y - 2 \\x = 6y + 8\end{cases}$

Solve each problem. Alcohol Mixture Barak wishes to strengthen a mixture that is 10% alcohol to one that is 30% alcohol. How much pure alcohol should he add to 12 L of the 10% mixture?

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.

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.

-2x = 6y + 18

-29 = 5y - 3x