SOLUTION: On my homework it says: Solve the system of equations through elimination. 2x-3y=21 -6x+2y=7 I have tried so many times but can't figure it out. And how do I know whether to

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: On my homework it says: Solve the system of equations through elimination. 2x-3y=21 -6x+2y=7 I have tried so many times but can't figure it out. And how do I know whether to       Log On


   



Question 1007851: On my homework it says:
Solve the system of equations through elimination.
2x-3y=21
-6x+2y=7
I have tried so many times but can't figure it out. And how do I know whether to add or subtract?
I'd greatly appreciate it if I could be taught HOW to solve this, not just the answer.
Thank You!

Found 2 solutions by tiffany222, MathLover1:
Answer by tiffany222(56) About Me  (Show Source):
You can put this solution on YOUR website!
2x - 3y = 21
-6x + 2y = 7
Step 1: Eliminate either x or y to solve for one value. In this problem, we will eliminate x by multiplying the first equation by 3.
6x - 9y = 63
-6x + 2y = 7
Step 2: Add the two equations to eliminate x and solve for y. We add because we want the x coefficient to become 0.
-7y = 70
y = -10
Step 3: Substitute the y value we just got into either one of the two original equations to get the x value. I decided to use the first equation, but using the second equation will also get you the right answer.
2x - 3y = 21
2x - 3(-10) = 21
2x + 30 = 21
2x = -9
x = -4.5
Final Answer:
x = -4.5
y = -10

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Solve the system of equations through elimination.
2x-3y=21.....eq.1.........both sides multiply by 3
-6x%2B2y=7.........eq.2
-----------------------------
6x-9y=63.....eq.1
-6x%2B2y=7.........eq.2
-----------------------------add both eq.1 and eq.2
6x-9y%2B%28-6x%2B2y%29=63%2B7
cross%286x%29-9y-cross%286x%29%2B2y=70.......eliminate 6x and -6x
-9y%2B2y=70
-7y=70
y=70%2F-7
highlight%28y=+-10%29
now go back to -6x%2B2y=7.........eq.2, substitute -10 for y and find x
-6x%2B2%28-10%29=7
-7-20=6x
-27=6x
x=-27%2F6
highlight%28x=-9%2F2%29 or highlight%28x=-4.5%29
so, these two lines intersect at point (-4.5,-10)