Question

Explain, in complete sentences, which method you would use to solve the following system of equations and why you chose that method. Show your work and provide the solution to the system.
5x + 3y = -7
4x - 2y = -10

Answer 1

There are several methods you could choose for this. I would choose to solve it in the following manner: (mainly because I don't like multiplying and making numbers bigger than I need them to be)

What I would do is subtract the second equation from the first. Doing so, I get:
x + 5y = 3

and ultimately:
x = 3 - 5y

Then, using the substitution method, I would input the expression for x into the first equation and isolate y:

5(3 - 5y) + 3y = -7
15 - 25y + 3y = -7
15 -(25 - 3)y = -7
15 -22y = -7
15 + 7 = 22y
22 = 22y
22/22 = y
1 = y

Then I would substitute the value for y into the one of the equations to find the value for x.

Answer 2

Thank you once again @Hero !

Answer 3

Did you find the value of x?