Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 12 - Matrices - 12-1 Adding and Subtracting Matrices - Practice and Problem-Solving Exercises - Page 768: 18

Answer

$x=2, $ $t=\dfrac{1}{10}$

Work Step by Step

Operating on the corresponding elements, the given matrix equation, $ \begin{bmatrix} 2 & 4 \\ 8 & 4.5 \end{bmatrix} = \begin{bmatrix} 4x-6 & -10t+5 \\ 4x & 15t+1.5x \end{bmatrix} ,$ implies the following equations: \begin{align*} \begin{array}{cc} 2=4x-6 &&4=-10t+5 \end{array} .\end{align*} Simplifying the equations above results to \begin{align*} \begin{array}{cc} 2+6=4x-6+6 &&4-5=-10t+5-5 \\ 8=4x &&-1=-10t \\ \dfrac{8}{4}=\dfrac{4x}{4} &&\dfrac{-1}{-10}=\dfrac{-10t}{-10} \\ 2=x &&\dfrac{1}{10}=t \end{array} .\end{align*} Hence, $ x=2, $ $t=\dfrac{1}{10} $.
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