How do I solve system of equations by substitution

3x-7y=41

x=-2y-21

(-5; -8)

Step-by-step explanation:

-6y-63-7y=41

-13y=104

y=-8

x=-2*-8-21=-5

Going off the value of x in terms of y given in the second equation, we can substitute the x in the first equation with the value - 2y - 21 to give us the equation

3 (-2y - 21) - 7y = 41

Distributing the 3 to the - 2y and - 12:

-6y - 63 - 7y = 41

Combining like terms:

-13y - 63 = 41

Adding 63 to either side:

-13y = 104

And dividing both sides by - 13:

y = - 8

We can plug in this solution for y to the second equation to obtain a solution for x:

x = - 2 (-8) - 21

x = 16 - 21

x = - 5

So our solution is the pair (-5, - 8).