Elimination Method

Question

-4x - 15y = -17

-x + 5y = -13

Answer 1

Multiply equation #2 by 4

Subtract the new equation from #1---this will eliminate the y terms and allow you to solve for x.

Once you have x, use either equation to find y

Answer 2

Alexis, the elimination method consists of (a) changing one equation do that one term equals the corresponding term in the other equation, and then (b) adding or subtracting the two equations do that terms cancels out, leaving only one term with a variable.

Here are two ways you could do that in this problem:

Eliminate x: Multiply the second equation by 4:

-4x - 15y = -17

-4x + 20y= -52

Now subtract the first equation from the second

0x + 35y = -35

You already know how to solve for y: Divide by 35

Y = -1

Now put that y value into one of the original equations and solve for x:

-4x -15*(-1) = -17

-4x + 15 = -17

-4x = -32

x = 8

”But Ed, how would I know to eliminate x? What would happen if I eliminated y instead?”

Alexis, it will come out the same, Fear not!

Eliminate y: Multiply the second equation by 3:

-4x - 15y = -17

-3x + 15y = -39

Now add the two equations

-7x + 0y = -56

solve for x

x = 8

Put the x value into one of the equations and solve for y.

-4x - 15y = -17

-32 - 15y = -17

-15y = 15

y = -1

So, the good news is, it doesn’t matter which one you eliminate first, you’ll get the same answers to the problem. In other words: You da boss! You can decide based on whatever looks like the easier arithmetic (that’s what I do, for many decades).

Answer 3

Step 1: Get either x or y to cancel out. In this case, we will use x.

-4x - 15y = -17

-4 (-x +5y = -13) Multiply -4 to get +4x. Negative and positive values cancel out. Multiply the rest

-------------------------

Step 2: Cancel out

-4x - 15y = -17

4x - 20y = 52

-------------------------------

-35y = 35

Step 3: Solve for y

-35y = 35 Divide -35 on both sides to get a positive 'y' value.

y = -1

Step 4: Plug in the 'y' value for any of the two equations to get the 'x' value.

Eqn 1: -4x - 15y = -17

-4x - 15(-1) = -17

-4x +15 = -17 Subtract 15 on both sides

-4x = - 32 Subtract -4 on both sides to get a positive 'x' value

x = 8

Eqn 2: -x + 5y = -13

-x + 5(-1) = -13

-x + -5 = -13 Add 5 on both sides to cancel out -5. This gets 'x' by itself.

+5 +5

--------------

-x = -8 Divide the negative from 'x' because you can't have a negative x value.

x = 8