Browse Questions

# If $\begin{bmatrix} x+3 & 4 \\ y-4 & x+y \end{bmatrix} = \begin{bmatrix} 5 & 4 \\ 3 & 9 \end{bmatrix}$, find 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:
$\begin{bmatrix} x+3 & 4 \\ y-4 & x+y \end{bmatrix} = \begin{bmatrix} 5 & 4 \\ 3 & 9 \end{bmatrix}$
The given matrices are equal,hence their corresponding elements should be equal.
x+3=5-----(1)
y-4=3------(2)
x+y=9------(3)
From equation (1) we have
x+3=5
x=5-3
x=2.
Step2:
From equation (2) we have
y-4=3.
y=3+4.
y=7.
x=2,y=7.