Question

Solve the system, using substitution. Write the solution as an ordered pair.

x = 2y - 2 and 3x - y = 14

Answer 1

An ordered pair is basically just a point written as (x,y)
Do you know how to solve this with substitution?

Answer 2

no

Answer 3

Ok, so substitution means to replace x or y for what you know x or y equals.
For example, the first equation is x = -2y - 2, here we know what x equals, so we can put that in for x in the second equation which is
3x -y= 14
3(-2y -2) -2 = 14
Now we can solve for y. Once we get y we can put that in for "y" in one of the equations to solve for x

This making sense?

Answer 4

yes

Answer 5

Ok, see if you can solve for y from the substituted equation which is:
3(-2y -2) -y = 14

Answer 6

im not good at solving things i freak under pressure.

Answer 7

Ninja, shouldn't the correct equation be 3(2y-2)-y = 14? Where is the -2y coming from? it should be positive.

Answer 8

i think lamaguineapig is right

Answer 9

Yes it should..sorry I meant to type a y there but accidentally typed 2. >.>

Answer 10

3(2y-2)-y=14
6y-6-y=14
5y-6=14
-6 -6
_____________
5y=8
im not 100% sure im doing this right

Answer 11

Yup, your almost right, but the last step you want to add 6 to both sides, so it should look like this
5y-6=14
+6 +6
----------
5y = 20
y = 4

Now you can put 4 in for y in one of those two equations.and solve for x! Try doing that. I'll double check your work for you. :)

Answer 12

thats where i messed up!

Answer 13

Yup. See if you can find x now. :)

Answer 14

6

Answer 15

Yup. I'll put it in the first equation to check it
x = 2y - 2
x = 2(4) - 2
x = 8 -2
x = 6

So now we can put x and y in (x,y) and we have our answer!

Answer 16

Here's a graph of the two lines. You can see that they intercept at (6,4) so our solution is correct!