Find x and y if: 4(5 x / −1 1) − 3(6 x / 2 2) = 2(1 4 / y −1)

Question

ScanSolve AI Tutor · Accepted Answer

Here's how to solve the matrix equation:

Perform the scalar multiplication for each matrix.
$4\begin{pmatrix} 5 & x \\ -1 & 1 \end{pmatrix} - 3\begin{pmatrix} 6 & x \\ 2 & 2 \end{pmatrix} = 2\begin{pmatrix} 1 & 4 \\ y & -1 \end{pmatrix}$ $\begin{pmatrix} 4 \times 5 & 4 \times x \\ 4 \times (-1) & 4 \times 1 \end{pmatrix} - \begin{pmatrix} 3 \times 6 & 3 \times x \\ 3 \times 2 & 3 \times 2 \end{pmatrix} = \begin{pmatrix} 2 \times 1 & 2 \times 4 \\ 2 \times y & 2 \times (-1) \end{pmatrix}$ $\begin{pmatrix} 20 & 4x \\ -4 & 4 \end{pmatrix} - \begin{pmatrix} 18 & 3x \\ 6 & 6 \end{pmatrix} = \begin{pmatrix} 2 & 8 \\ 2y & -2 \end{pmatrix}$
Perform the matrix subtraction on the left side.
$\begin{pmatrix} 20 - 18 & 4x - 3x \\ -4 - 6 & 4 - 6 \end{pmatrix} = \begin{pmatrix} 2 & 8 \\ 2y & -2 \end{pmatrix}$ $\begin{pmatrix} 2 & x \\ -10 & -2 \end{pmatrix} = \begin{pmatrix} 2 & 8 \\ 2y & -2 \end{pmatrix}$
Equate the corresponding elements to find $x$ and $y$ .
From the first row, second column:
$x = 8$
From the second row, first column:
$-10 = 2y$
Solve for $y$ .
$2y = -10$ $y = \frac{-10}{2}$ $y = -5$
The values are $x = 8$ and $y = -5$ .
$\boxed{x = 8, y = -5}$

Find x and y if: 4(5 x / -1 1) - 3(6 x / 2 2) = 2(1 4 / y -1)