Answer to Question #211539 in Algebra for Moe

Question

If Let $\begin{pmatrix} 2 & 1 \\ 5 & 3 \end{pmatrix}\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 2 \\ 4 \end{pmatrix}$,

Solve for x and y

Answer 1

​$\begin{pmatrix} 2 & 1 \\ 5 & 3 \end{pmatrix}\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 2 \\ 4 \end{pmatrix}$

Performing matrix multiplication

$\begin{pmatrix}2 x+y \\5x+3 y \end{pmatrix} = \begin{pmatrix} 2 \\ 4 \end{pmatrix}$

Equating corresponding elements we get

2x + y = 2 ••••••••••(1)

5x + 3y = 4. ••••••••••(2)

Multiplying equation (1) by 3 we get

6x + 3y = 6 ••••••••••(3)

Then subtracting equation (2) from equation (3) we get

6x + 3y - 5x - 3y = 6 - 4

=> x = 2

Substituting x = 2 in equation (1) we get

4 + y = 2

=> y = 2 - 4 = - 2

So solution is x = 2 and y = -2