Lesson 12 Solving Systems with Matrices Practice Understanding

Ready

1.

Set up a matrix that goes with the situation described.

A theater wants to take in $$ 2,000$ for a certain matinee. Children’s tickets cost $$ 5$ each and adult tickets cost $$ 10$ each. If the theater has a maximum of $350$ seats, write a system of equations that can be solved to determine the number of both children and adult tickets the theater can sell.

Set

Assume that the matrices given represent linear systems of equations. Practice the strategy you used for row reduction of a given matrix so that the left portion of the matrix (the 2 rows and first 2 columns of entries) has $1$ ’s on the diagonal. Write a description of what you did to get from one matrix to another in each step of your sequence of matrices.

2.

$[\begin{array}{r} 3 & 2 \\ 1 & 2 \end{array} | \begin{array}{r} - 6 \\ 2 \end{array}] R_{1} - R_{2} \to R_{2} [\begin{array}{r} 3 & 2 \\ 2 & 0 \end{array} | \begin{array}{r} - 6 \\ - 8 \end{array}] R_{2} \div 2 \to R_{2} [\begin{array}{r} 3 & 2 \\ 1 & 0 \end{array} | \begin{array}{r} - 6 \\ - 4 \end{array}] \to$

3.

$[\begin{array}{r} - 3 & 1 \\ 2 & 3 \end{array} | \begin{array}{r} - 12 \\ - 14 \end{array}] 3 R_{1} - R_{2} \to R_{2} [\begin{array}{r} - 3 & 1 \\ - 11 & 0 \end{array} | \begin{array}{r} - 12 \\ - 22 \end{array}] \to$

4.

$[\begin{array}{r} 7 & 2 \\ 8 & 2 \end{array} | \begin{array}{r} 24 \\ 30 \end{array}] \to$

5.

$[\begin{array}{r} 5 & 1 \\ 10 & - 7 \end{array} | \begin{array}{r} 9 \\ - 18 \end{array}] \to$

Go

Solve each system of equations using a method of your choice.

6.

${\begin{cases} x - y = 11 \\ 2 x + y = 19 \end{cases}$

7.

${\begin{cases} 8 x + y = - 16 \\ - 3 x + y = - 5 \end{cases}$

8.

${\begin{cases} - 4 x + 9 y = 9 \\ x - 3 y = - 6 \end{cases}$

9.

${\begin{cases} - 7 x + y = - 19 \\ - 2 x + 3 y = - 19 \end{cases}$