Need help solving the system of equations by either substitution or elimination...?

Question

Problem:
3x= -31 + 2y
5x + 6y = 23

I know how to solve system of equations, but I'm stuck on this problem. Could you help me out?

Answer 1

First, combine by getting the same things on the same sides:
3x - 2y = -31
5x + 6y = 23
Now multiply the first equation by 3 to make the -2y into -6y so it will cancel the other equation's +6y
9x - 6y = - 93 now add the 2 equations
5x + 6y = 23

14x = -70
so x = -5
now you can substitute into the equation
5(-5) +6y = 23
so 6y = 48
and y = 8

Answer 2

3(3x - 2y = -31) subtract 2y, multiply everything by 3 to use substitution on the first equation

9x - 6y = -93
5x + 6y = 23

14x = -70
x = -5

5(-5) + 6y = 23
-25 + 6y = 23
6y = 48
y = 8

(-5, 8) is the solution

Answer 3

Substitution: a million/2 x + a million/2 y = 7 ............ (a million) a million/2 x - a million/2 y = -2 ............ (2) x = 2(7 - a million/2 y).................(3) substitute (2) a million/2[2(7 - a million/2 y)] - a million/2 y = -2 7 - a million/2 y - a million/2 y = -2 7 - y = -2 -y = -9 y = 9 substitute (3) x = 2(7 - a million/2 y) x = 2(7 - a million/2 [9]) x = 2(7 - 4.5) x = 14 - 9 x = 5 removal a million/2 x + a million/2 y = 7 ............ (a million) a million/2 x - a million/2 y = -2 ............ (2) (a million) - (2) 2 (a million/2 y) = 7 - -2 y = 9 substitute (a million) a million/2 x + a million/2 (9) = 7 a million/2 x + 4.5 = 7 a million/2 x = 2.5 x = 5

Answer 4

Solve for x on both, then set them equal to eachother.

Answer 5

the answer is (-5, 8)