Question

Solve the following system of equations using an inverse matrix. You must also indicate the inverse matrix, A-1, that was used to solve the system. You may optionally write the inverse matrix with a scalar coefficient.

Answer 1

$\begin{cases}5x-3y={8} \\ 7x-5y={4}\end{cases}$

start multiplying the first equation by 7 and the second by 5

$\begin{gathered} 7\ast(5x-3y=8) \\ 5\ast(7x-5y=4) \\ then, \\ 35x-21y=56 \\ 35x-25y=20 \end{gathered}$

then, subtract both of the equations,

$\begin{gathered} 35x-21y-(35x-25y)=56-20 \\ -21y+25y=36 \\ 4y=36 \end{gathered}$

solve for y

$\begin{gathered} y=\frac{36}{4} \\ y=9 \end{gathered}$

substitute in the first equation,