# Chapter 12 - Data Analysis and Probability - 12-1 Organizing Data Using Matrices - Practice and Problem-Solving Exercises - Page 731: 31

$x=-2$ $y=5$

#### Work Step by Step

For the equation below to be true, the corresponding numbers in the first two matrices added together must equal the corresponding number in the final matrix. Lets use: $x+4y=18$ $2x+y=1$ Solve for y with the second equation: $y=1-2x$ Substitute the equation for y into the first equation: $x+4(1-2x) = 18$ Then solve for x: $x+4(1-2x) = 18$ $x+4-8x=18$ $4-8x+x=18$ $4-7x=18$ $-7x=18-4$ $-7x=14$ $x=\frac{14}{-7} =-2$ Now substitute -2 in place of x in the second equation to find y: $y=1-2x$ $y=1-2(-2)$ $y= 1+4$ $y=5$

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