Help solving linear systems by elimination?

5x - 4y = -7

5x + 3y = 14

Just find any way to add the equations or subtract one from another so that you have only one variable to solve for. The coefficients of a variable need to have equal absolute value in both equations for you to do this.

Here you can just subtract either of the equations from the other one to eliminate x as 5x - 5x will leave you with only y and have y to solve for.

0x -7y = -21

-7y = -21

y = 3

Get this back to the original equations to solve for x.

5x + 3y = 14

x = (14 - 3*y)/5 = (14 - 3*3)/5 = 1

Check for (1, 3):

5*1 - 4*3 = -7

5 - 12 = -7 OK

5*1 + 3*3 = 14

5 + 9 = 14 OK

x+y=5

2x-5y=17

Here you can't just subtract one from another or add because nothing would be eliminated. The coefficients don't have the same absolute value. So let's multiply the first equation with 2. Which gives:

2x + 2y = 10

2x - 5y = 17

Now subtract in any order, say 2nd from first.

0x + 2y -(-5y) = -7

7y = -7

y = -1

Solve for x.

x + y = 5

x = 5 - y

x = 5 -(-1)

x = 6

(6, -1)

Check... did. You can do it, too.

Hope that helped.