Question

For what value of x and y is the matrix equation [y 8x] = [15+x 2y] true?

Answer 1

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:

`\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}`

Using the value of y from the first equation in the second one, we have:

`\begin{gathered} 8x=2(15+x) \\ 8x=30+2x \\ 8x-2x=30 \\ 6x=30 \\ x=(30)/(6)=5 \end{gathered}`

Finding the value of y, we have:

`\begin{gathered} y=15+x \\ y=15+5 \\ y=20 \end{gathered}`

So we have that x = 5 and y = 20.