Question

Solve the following using the elimination method. If the system has an infinite number of solutions, use set-builder notation to write the the solution set. If the system has no solution, state this:

1) 3x - 5y = -3
-9x + 15y=9

2) 7x + 9y = -27
-2x - 7y = 21

Answer 1

1) multiply first equation by 3, so your system:
9x-15y=-9
-9x+15y=9
if you add them : 0=0
so your first eq=second one.
no solution
2) multiply first eq by 2 & second by 7
14x+18y=-54
-14x-49y=147
add them:
0-31y=93
-31y=93
divide both sides by (-31):
y=-3
substitute value of y in any original eq:
9*x-15*(-3)=-9
9x+45=-9
9x=-54
x=-6
solution:
x=-6, y=-3

Answer 2

thank you

Answer 3

wouldn't you plug y into the equation 14x + 18y = -54 instead of 9x - 15y = -9? I'm confused