# If $\begin{bmatrix} 15 & x+y \\ 2 & y \end{bmatrix} = \begin{bmatrix} 15 & 8 \\ x-y & 3 \end{bmatrix}$find the value of x and y

Toolbox:
• If the order of 2 matrices are equal, their corresponding elements are equal, i.e, if $A_{ij}=B_{ij}$, then any element $a_{ij}$ in matrix A is equal to corresponding element $b_{ij}$ in matrix B.
• We can then match the corresponding elements and solve the resulting equations to find the values of the unknown variables.
Step1:
Given
$\begin{bmatrix} 15 & x+y \\ 2 & y \end{bmatrix} = \begin{bmatrix} 15 & 8 \\ x-y & 3 \end{bmatrix}$
$\Rightarrow$ x+y=8-----(1)
y=x-y-------(2)
From equation (2) we have
y=x-y.
y+y=x
x=2y-----(3)
Step2:
Substitute the value of x in equation (1)
x+y=8
2y+y=8
3y=8
y=8/3
Step3:
Substitute the value of y in equation (3)
x=2y
x=2(8/3)
x=16/3
x=16/3 y=8/3