Question

find x and y.
\\(\

$$\begin{bmatrix} x + 2 & 3 & 6 \\\\ -7 & 2y & 2x \\\\ 7 & 5 & y + 2 \\end{bmatrix}$$

= \

$$\begin{bmatrix} 2x + 6 & 3 & 6 \\\\ -7 & 0 & -8 \\\\ 7 & 5 & 2 \\end{bmatrix}$$

\\)
\\(x = \boxed{}\\)
\\(y = \boxed{}\\)
resources
read it watch it master it

Explanation:

Step1: Solve for \( x \) using first row

For two matrices to be equal, their corresponding elements must be equal. Looking at the first element of the first row: \( x + 2 = 2x + 6 \)
Subtract \( x \) from both sides: \( 2 = x + 6 \)
Subtract 6 from both sides: \( x = 2 - 6 = -4 \)

Step2: Verify \( x \) with third column

Check the third element of the second row: \( 2x = -8 \)
Substitute \( x = -4 \): \( 2(-4) = -8 \), which is true. Also check third element of third row: \( y + 2 = 2 \), so \( y = 0 \). Wait, also check second row second element: \( 2y = 0 \), so \( y = 0 \) (consistent). Let's confirm \( x \) again with first row: \( x + 2 = -4 + 2 = -2 \), \( 2x + 6 = 2(-4) + 6 = -8 + 6 = -2 \), which matches.

Step3: Solve for \( y \) using second row

From the second element of the second row: \( 2y = 0 \)
Divide both sides by 2: \( y = 0 \)

Answer:

\( x = -4 \)
\( y = 0 \)