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Sagot :
In order to find the values of x and y so the matrix equation is true, we need to equate each corresponding elements of the matrices. So we have that:
[tex]\begin{gathered} \begin{bmatrix}{y} \\ {8x}\end{bmatrix}=\begin{bmatrix}{15+x} \\ {2y}\end{bmatrix} \\ \mleft\{\begin{aligned}y=15+x \\ 8x=2y\text{ }\end{aligned}\mright. \end{gathered}[/tex]Using the value of y from the first equation in the second one, we have:
[tex]\begin{gathered} 8x=2(15+x) \\ 8x=30+2x \\ 8x-2x=30 \\ 6x=30 \\ x=\frac{30}{6}=5 \end{gathered}[/tex]Finding the value of y, we have:
[tex]\begin{gathered} y=15+x \\ y=15+5 \\ y=20 \end{gathered}[/tex]So we have that x = 5 and y = 20.
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