Solve the following systems of

Question

Solve the following systems of equations by matrix method $$2ax-2by=-a-4b$$ and $$2bx+2ay=4a-b$$

I only need the equation in terms of $x$ and $y$ in order to represent in the matrix form but how can I eliminate $a$ and $b$.

Answer 1

I don't see the point why you need it in the form of only $x$ and $y$ since you can write and row reduce the following:

$$ \begin{bmatrix}2a & -2b & -a-4b \\2b & 2a & 4a-b \end{bmatrix}$$

Answer 2

Take $2a$ times (both sides of) your first equation and add it to $2b$ times the second equation:

$$4(a^2+b^2)x=-2a^2-2b^2$$

Divide to solve for $x$.

Take $2b$ times your first equation and subtract $2a$ times the second equation:

$$-4(a^2+b^2)y=-8a^2-8b^2$$

Divide to solve for $y$.