Question

find the solution of the system of equations.
$-10x - y = -29$
$10x + 7y = 23$

Explanation:

Step1: Add the two equations

We have the system:
$$-10x - y = -29$$
$$10x + 7y = 23$$
Adding them together: $(-10x - y)+(10x + 7y)=-29 + 23$
Simplify left side: $(-10x+10x)+(-y + 7y)=6y$
Right side: $-6$
So we get $6y=-6$

Step2: Solve for y

Divide both sides of $6y=-6$ by 6:
$y=\frac{-6}{6}=-1$

Step3: Substitute y into one equation to find x

Substitute $y = -1$ into the first equation $-10x - y=-29$:
$-10x-(-1)=-29$
Simplify: $-10x + 1 = -29$
Subtract 1 from both sides: $-10x=-29 - 1=-30$
Divide both sides by -10: $x=\frac{-30}{-10}=3$

Answer:

The solution is $x = 3$, $y=-1$ (or as an ordered pair $(3, -1)$)