# Populate matrix from linear system

What is the strategy to populate a matrix from a linear system of equations?

As a toy example, I have some scary, complicated math, that generates eq1 and eq2. I can solve this, linear, system using Solve. I want to inspect the matrix that is made before the Solve step. In my application I expect this to be a system to be over defined.

eq1 = a x + y;
eq2 = b x - y;
Solve[{eq1 == 7, eq2 == 1}, {x, y}]


In the toy example, it would be this matrix:

( {
{a, 1},
{b, -1}
} ) // MatrixForm


I could imagine parsing the text or something wacky like that.

CoefficientArrays[{eq1, eq2}, {x, y}][[2]] // Normal