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If [[2, -y-4], [3, x+y]] = [[7, 4], [3, 9]] find the value of x and y.

August 29, 2026Mathematics

ScanSolve AI Answer

Answer

x=20, y=-11

3 steps

To find the values of $x$ and $y$ , we equate the corresponding elements of the two matrices.

Given the matrix equality:

\begin{bmatrix} 2 & -y-4 \\ 3 & x+y \end{bmatrix} = \begin{bmatrix} 2 & 7 \\ 3 & 9 \end{bmatrix}

Equate the elements in the top right position.
$-y-4 = 7$
Add 4 to both sides:
$-y = 7 + 4 \\ -y = 11$
Multiply by -1:
$y = -11$
Equate the elements in the bottom right position.
$x+y = 9$
Substitute the value of $y = -11$ into this equation:
$x + (-11) = 9 \\ x - 11 = 9$
Add 11 to both sides:
$x = 9 + 11 \\ x = 20$
State the values of $x$ and $y$ .
The values are $x = 20$ and $y = -11$ .

The final answer is $x=20, y=-11$ .

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