SOLUTION: Hello out there,I need some help with some problems,the first one is,Use elimination to solve:3x-y=15 and 5x+y=9.The next one is,Use elimination to solve:3x-2y=6 and x-2y=-2.The ne

Algebra ->  Linear-equations -> SOLUTION: Hello out there,I need some help with some problems,the first one is,Use elimination to solve:3x-y=15 and 5x+y=9.The next one is,Use elimination to solve:3x-2y=6 and x-2y=-2.The ne      Log On


   

Question 103038: Hello out there,I need some help with some problems,the first one is,Use elimination to solve:3x-y=15 and 5x+y=9.The next one is,Use elimination to solve:3x-2y=6 and x-2y=-2.The next one is,Use elimination to solve:x/2+2y=9 and 2x-y=18.And the last one is,Use elimination to solve:4x-y=-3 and 5x+2y=-20.Thanks to whoever can help.
Found 2 solutions by MathLover1, elima:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

1.
add 3x-y=15
+ 5x%2By=9
_____________
= > 8x+=+24 = > x+=24%2F8 = > x+=+3
2.
Subtract
3x-2y=6+
- x-2y=-2
______________
2x+=+8
x+=+4
3.
x%2F2%2B2y=9 (this one multiply by 2)
2x-y=18 (this one multiply by 4)
Then we have
x%2B4y=18
8x-4y=72+ now add them
x%2B4y=18
+ 8x-4y=72
__________
9x+=90
x=10
4.
4x-y=-3 (this one multiply by 2 and add them
5x%2B2y+=-20
We will have
8x+%96+2y+=+-6
+ 5x%2B2y+=-20
_________________
13x+=+-26
x+=+-2

Answer by elima(1433) About Me  (Show Source):
You can put this solution on YOUR website!
Solving by elimination, means you want to eliminate one of the variables.
1)3x-y=15 and 5x+y=9
We first set up the equations so they are being added together;
3x-y=15
5x+y=9
_______
8x=24
x=3
Now we substitute 3 for x in either equation;
5(3)+y=9
15+y=9
y=9-15
y=-6
2)3x-2y=6 and x-2y=-2
3x-2y=6
x-2y=-2
________
Since just by adding these two together will not eliminate a variable we need to multiply one of the equations by something that will make one of the variables cancel out. In this case lets multiply the second equation by -1;
-1(x-2y=-2)
-x+2y=2
Now we can add them together canceling out one of the variables;
3x-2y=6
-x+2y=2
_________
2x=8
x=4
x-2y=-2
4-2y=-2
-2y=-2-4
-2y=-6
y=3
3)x/2+2y=9 and 2x-y=18
Lets multiply the first equation by -4, so we can get rid of the fraction;
-4(x/2+2y=9)
-2x-8y=-36
now lets add them together
-2x-8y=-36
2x-y=18
________
-9y=18
y=-2
2(-2)-y=18
-4-y=18
-y=14
y=-14
4)4x-y=-3 and 5x+2y=-20
Multiply the first equation by 2;
2(4x-y=-3)
8x-2y=-6
Now add;
8x-2y=-6
5x+2y=-20
_________
13x=-26
x=-2
4(-2)-y=-3
-8-y=-3
-y=-3+8
-y=5
y=-5
Hope you got it all
:)