I need help with Elmination

Confusedaboutalgabra said:

1:Line up the like terms
2: Make the coefficient on one of the varibels the same by multiplying.
3:add/subtract the 2 equations
4:solve for the varibel
5:find the other Varibel

Those are my rules to follow when attempting to do elimination problems, but I'm confused about steps 2,3,and 5.

Code:

example.... 5x-8y = 25.....................(1)
                  -x+4y = -7 ....................(2)

okay the like terms are lined up. Now this is where I get stuck.

I'm going to focus on the "x" varibel, I know that theres a 1 infront of the -x. so im going to add 5x plus -1x which = 4x(No..).

2: Make the coefficient on one of the varibels the same by multiplying.

The coefficients of 'x' are (you chose to focus on x) - (-1) and (5)

So multiply equation 2 by 5

Code:

                 5x -    8y = 25.....................(1)
                -5x + 20y = -35 ....................(3)

3:add/subtract the 2 equations

Add (1) and (3) to get

Code:

                  12y = -10 ....................(4)

4:solve for the varibel
Solve for 'y' - noticed you focussed on 'x' to be eliminated - so you get to solve for 'y' first.

Code:

                  y = -5/6 ....................(5)

5:find the other Varibel
Now use (5) in (2) get 'x'

Code:

                  - x + 4y = -7............................(2)
                  -x + 4*(-5/6) = 7
                  -x - 20/6 = -7
                       x = 22/6.................................(6)

There is one other important step

6: Check answers by using the values found for the variables back into the equations.

Code:

                 5x -8y = 25.....................(1)
                -x + 4y = -7 ....................(2)

  5*(22/6) -8*(-5/6) = 110/6 + 40/6 = 150/6 = 25 ................(1)checks
-(22/6) + 4(-5/6) = -22/6 - 20/6 = -42/6  = -7 ......................(2)checks

Then I would ignore the ys for now and solve for the 2 numbers at the end of the problem.

So 25+-7=18, right? so 4x=18

so now Ill pick the top problem and rewrite it as 5(4)-8y

5 times 4 is 20

then this is where I get Stuck do i minus 20 from 8y? or divide somehow?

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