[Math] How to solve a linear equation with two unknowns when it is not a square matrix

Question

I am given the following two equations and am asked to solve for $x_1$ and $x_2$ using $A^{-1}$ (inverse method) of a matrix.

$$x_1 + 2x_2 = 1$$

$$3x_1 + 4x_2 = 5$$

how would you solve something like this? I thought to be able to do the inverse you would have to have a square matrix, and wouldn't this be a $2\times 3$ matrix?

Answer 1

Hint:

you have the equation:

$$[x_1,x_2]\left[\begin{eqnarray*} 1,3\\2,4 \end{eqnarray*}\right]=[1,5]$$