Question

y = -2x + 19
y = x + 7


x = 4, y = 11
x = -12, y = -5
x = -4, y = 3
x = 8, y = 3

Answer 1

Do you know methods of substitution and elimination to solving a system of 2 equations?

Answer 2

No, I don't know how to do it.

Answer 3

That's okay, I'll show you :)

Answer 4

Alright thank you!

Answer 5

One method is substitution. This means that we substitution one variable into the other. In your case, we see that y=x+7. That means we can plug in x+7 for y in the other equation!

\[\huge y=-2x+19\]
Substituting:
\[\huge x+7=-2x+19\]
Solving for x, we get:
\[\huge 3x=12 \rightarrow x=4\]
Then we can plug in x=4 back into any of the equations. And find y
\[\huge y=x+7 \rightarrow y=4+7=11\]

Answer 6

So, just solve one at a time and then plug the answers back in. and x=4 and y=11

Answer 7

we substitute*

Answer 8

it makes sense now

Answer 9

And yes :)

Answer 10

Thank you!

Answer 11

There's also another method called elimination. When we approach the problem using elimination, we try to multiply one of the equations by a number such that when we add the two equations, one of the variable cancels out.

y = -2x + 19
y = x + 7

What do you think? We can either multiply one of them by (-1) so that when we add them, the y's cancel out. Or we can multiply the bottom equation by (2) so that when we add them the x's cancel out. Let's try cancelling out the x's.
So,

y = -2x + 19
2y = 2x + 14

When we add this two equations, we get

3y = 33
y = 11

Now when we plug this back into any of the equations, we should see that x = 4.

If you're ever in doubt whether your answer is correct, you should try to try the other method and see if your answers match. Both will always yield the same answer. Depending on the difficulty of the problems or how complicated they are, sometimes it's even easier to approach it using elimination even though students tend to fear it more than substitution because it's a new method to them. I recommend getting comfortable with elimination because as you can see, we actually did LESS math and algebra than we did with substitution. Hope this helps :)

Answer 12

The second seems a little harder lol

Answer 13

You would think so! It's newer approach to students and we're so used to systematically plugging in values into other parts to solve. But it really is easier in the long run! The "hardest" part is determining what equation to multiply but which number. Sometimes you have to multiply both equations. For instance, if you have
4y = 4x + 2
3y = 7x + 9

You can see that we can't multiply only one of the equations to get the other.
We could multiply the top by (-3) or the bottom by (-4) so that the y's cancel out.
OR we could multiply the top by (-7) or the bottom by (-4) so that the x's cancel out.
You can see that if we tried this using substitution, we'd get fractions and it's easy to get confused and mess up when multiplying or dividing fractions. Therefore, by using elimination, we can do hardly any algebra and still get our answer :)

Answer 14

I meant to say that we'd have to multiply the top and the bottom*
So we could multiply the top by (-3) AND the bottom by (-4). you have to do both so that you get -12y+12y when you add the two equations if you wanted to eliminate y