Question

Solve the following pair of simultaneous equations using the matrix method. 4x + 3y = 0 x + 2y = 5 [3] Total: 5 marks

Answer 1

we have the system of equations

4x+3y=0

x+2y=5

Convert to matrix form

$A\cdot X=B$

matrix A

$A=\begin{bmatrix}{4} & {3} \\ {1} & {2}\end{bmatrix}$

matrix X

$X=\begin{bmatrix}{x} & {} \\ {y} & {}\end{bmatrix}$

matrix B

$B=\begin{bmatrix}{0} & {} \\ {5} & {}\end{bmatrix}$

substitute

$\begin{bmatrix}{4} & {3} \\ {1} & {2}\end{bmatrix}\cdot\begin{bmatrix}{x} & {} \\ {y} & {}\end{bmatrix}=\begin{bmatrix}{0} & {} \\ {5} & {}\end{bmatrix}$

Find out the determinant of matrix A

D=4*2-3*1

D=5

Find out the determinant Dx

$Dx=\begin{bmatrix}{0} & {3} \\ {5} & {2}\end{bmatrix}=-15$

Find out the determinant Dy

$Dy=\begin{bmatrix}{4} & {0} \\ {1} & {5}\end{bmatrix}=20$

Find out the value of x

x=Dx/D

x=-15/5=-3

Find out the value of y

y=Dy/D

y=20/5=4

therefore

The solution is (-3,4)