Algebra 1 - Assessment #2 - Systems that use Elimination

Question

Solve using elimination. Show all of your work!

#1 7x+2y=24 8x+2y=30

#2 9x-4y=11 x-3y=-9

*Please help! I'm really struggling, and this was due yesterday! Ive asked other people but they use a different way then my teacher does, I just cant fail this, please if you can help. Also theres another word problem that comes with it.

Answer 1

Let's go through the first problem step-by-step. In the elimination method we want to "eliminate" one of the variables to get the answer to the other variable. Then we take that answer and solve either one of the equations for the other variable.

We have:

Eq. I: 7x + 2y = 24

Eq. II: 8x + 2y = 30

Notice that both equations have a "+2y" in them. If we were to subtract the first equation from the second we could solve for "x".

8x + 2y = 30

-(7x + 2y = 24)

x = 6

Using this value for "x" in either of the equations we can solve for "y":

7x + 2y = 24 Eq. I

7(6) + 2y =24 substitute 6 for "x"

42 + 2y = 24

2y = 24 -42 subtract 42 from both sides

2y = -18

y = -18/2 divide both sides by 2

y = -9

Therefore, your answer is x = 6 and y = -9. Written in coordinate form it would be (6,-9).

The second problem is a little trickier because you need to determine which variable you want to eliminate when neither equation has the same value in front of the variables.

Eq. I: 9x - 4y = 11

Eq. II: x - 3y = -9

If we were to multiply everything in Eq. II by -9 and then add the 2 equations together, we could solve for "y":

x - 3y = -9 Eq, II

-9(x - 3y = -9) multiply Eq. II by -9

-9x + 27y = 81 result

Now, add this to Eq. I and solve for "y":

9x - 4y = 11 Eq. I

+(-9x + 27y = 81) "new" Eq. II

23y = 92 result

y = 92/23 divide both sides by 23

y = 4 answer for "y"

Putting this value of "y" back into either equation yu can now solve for "x":

x - 3y = -9 original Eq. II

x - 3(4) = -9 substitute 4 for "y"

x - 12 = -9

x = -9 + 12 add 12 to both sides

x = 3 answer for "x"

Check these values by putting them into each equation and the answers should be correct.

Hope this helps!

Answer 2

These confused the heck out of me when I first learned it!

What we want to do is create opposites with one variable so that when we add the 2 functions, that variable cancels out. We can do that by multiplying one or both functions by something.

7x + 2y = 24

8x + 2y = 30

Simple enough! We can multiply either the top or bottom by -1. I'll do the bottom.

7x + 2y = 24

-8x - 2y = -30

-x = - 6

x = 6

Now, substitute 6 for x into either equation and solve for y.

Go!