Question

Solve by substitution: -5x + y = -2 -3x + 6y = -12 please explain

Answer 1

First we pick the equation. Let's say we pick first one. From it we express y.

$-5x+y=-2\Longrightarrow y=-2+5x$

Then we use this y and plug it in instead of y in the second equation.

$-3x+6(-2+5x)=-12$

Now just solve for x.

$-3x-12+30x=-12 \\-3x=-30x \\\underline{x=10}$

We plug this x in the first equation.

$-5\cdot10+y=-2$

And solve for y.

$-50+y=-2 \\\underline{y=48}$

So the solution to the equation is geometrically a point P which lies on the intersection of the two lines.

$\boxed{P(10,48)}$

Hope this helps.

r3t40