Question

-3x+7y=-36 -3x+2y=-36 find the solution of this system of equations

Answer 1

The answer is $(x.y) = (12,0)$.

Since the right hand sides of the two equations are the same, the left hand sides must be the same as well.

In other words, is the expression $-3x+7y$ equals -36 and so does the expression $-3x+2y$, then the two expression must equal each other, since they are two different ways of writing the same number. It's just like saying that 10+3 = 15-2, because they both represent the number 13.

So, we have

$-3x+7y = -3x+2y$

We can add 3x to both sides to simplify it. We're left with

$7y = 2y \iff 5y = 0 \iff y = 0$

Since we found the value for y, we can plug it in one of the two equations to deduce the value for x. For example, let's choose the first equation to get

$-3x+7\cdot 0=-36 \iff -3x = -36 \iff x = 12$