Question

Solve the system of equations using the elimination method and give your answer as an ordered pair:

2x + 10y = -42

-3x + 9y = -81

Answer 1

depending on which you want to eliminate first, either x or y, doesn't matter
In this case I want to eliminate x first to find y
to eliminate x in two equation, you need to have the same coeficient of x. rite now, the 1st one has 2 and 2nd one has -3
to make them equal, you need to multiply the 1st equation with 3, and the 2nd one with 2
note that once you multiply the equation with a number, you will need to multiply it to every variable of the equation
So multiply 1st one with 3 and 2nd one with 2, you have
6x + 30y = -126
-6x + 18y = -162
now they have the same coefficient of x, you can add two equation together to have:
(6x + (-6x) + (30y + 18y) = -126 + (-162)
=> 0x + 48y = -288
-> y = -288/48
-> y = 6
now you can plug y=6 back to equation 1 or 2, doesn't matter
I plug y=6 back into the 1st equation to get:
2x + 10y = -42
-> 2x +10*6 = -42
->2x + 60 = -42
->2x = -102
->x = -102/2
->x= -52
final answer: x=-52 and y = 6
plug these results back to the two equations, you will see that the results satisfy the two equation

Answer 2

thank yhu very much!!!