linear combination?

Question

2x-7y=3
5x-4y=-6

Answer 1

if i can remember linear combination, i think this is what you do (it has been a while since i was in a math class):

1. figure out how to get rid of one of the variables:
do this by figuring out the lowest common factor...in this case it is +/-10, and you want them to be the opposite so they will cancel each other out:
(2x-7y=3)5
(5x-4y=-6)-2
that gives you:
10x-35y=15
-10x+8y=12

2. you combine the two to get one equation:
-27y=27

3. solve for the variable that is left (in this case y):
y=27/-27
y=-1

4. put the variable you solved for back into one of the original equations to find the other variable...it does not matter which one you use, if you found the other variable correctly it will come out the same:
2x-7(-1)=3
2x+7=3
2x=-4
x=-2

5x-4(-1)=-6
5x+4=-6
5x=-10
x=-2

Answer 2

2x - 7y = 3
5x - 4y = -6

Multiply top by -5 and bottom by 2

-10x + 35y = -15
10x - 8y = -12

27y = -27
y = -1

2x - 7(-1) = 3
2x + 7 = 3
2x = -4
x = -2

ANS : (-2,-1)

Answer 3

On the first equation, subtract 2x on both sides:
-7y=-2x+3

Divide -7 on both sides:
y=2/7x-3/7

Plug that into the y-value:
5x-4(2/7x-3/7)=-6
5x-8/7x+12/7=-6
35/7x-8/7x+12/7=-6
27/7x+12/7=-6
27/7x=-42/7-12/7
27/7x=-54/7
(7/27)27/7x=(7/27)-54/7
x=-54/27
x=-2

Plug it into x:
5(-2)-4y=-6
-10-4y=-6

Add 10 to both sides:
-4y=4
y=-1
(-2,-1)

Check:
2(-2)-7(-1)=3
-4+7=3
3=3

5(-2)-4(-1)=-6
-10+4=-6
-6=-6

Answer 4

5(2x-7y=3)
-2(5x-4y= -6
so you get..

10x-35y=15
-10x+8y=12

27y=27....y = 1

so 10x-35(1)=15
10x-35=15
10x=50
x=5

so all in all, y=1 and x=5

Answer 5

-5(2x-7y)=3
2(5x-4y)= -6
-10x+35y= -15
10x-8y= -12
27y=-27
y=1
sub 1 for y
2x-7(1)=3
2x-7=3
2x=10
x=5

(5,1)

Answer 6

Do you want to solve this ? If so what method ? Matrices, substitution, etc?