Question

What are the solutions of the system?

Answer 1

A. (1, 0) and (–6, –28)
B. (1, 20) and (6, 0)
C. (1, 0) and (6, 20)
D. no solution

Answer 2

@JakeV8 can you help me

Answer 3

Sure, I would be happy to help. Did you get my name from someone :) Or did we already work together... it runs together sometimes :)

This is the problem, right?
y = x^2 - 3x + 2
y = 4x - 4

Answer 4

@JakeV8, I seen you were looking at my problem. So i was asking if you might be able to help me.
And yes that is the problem

Answer 5

Glad to help... :) give me a sec

Answer 6

Ok, ready? :)

Answer 7

Solutions to the system are points that satisfy both of the expressions you are given.

The way to find them is to find where these two curves (the first is a curve, the second is a line) intersect.

The way to find that is to realize that the places they intersect are points, so an (x,y) point that is an intersection "sits on" both curves/lines... it SATISFIES both expressions because at the point the cross, the point is on both lines.

So...what to do... ?

Answer 8

What you do is...

both expressions are like "y = " such and such, right? two expression where y is equal something.

But both are equal to y... so set the 2 expressions equal to each other, because y = y

Are you with me so far?

Answer 9

I assume you're reading or just waiting for a solution...

Answer 10

So I will give you more... but if you just grab the multiple choice answer and move on, you're missing out on a good chance to learn this stuff...

Answer 11

Setting the two expressions of y = "stuff" equal to each other gives:
4x - 4 = x^2 - 3x +2
simplifying by putting it all on the right side gives:
0 = x^2 - 3x - 4x + 2 + 4
which simplifies further to:
0 = x^2 -7x +6
and that can factor to:
0 = (x-6) (x-1)

The above expression is true when x = 6 or when x = 1 because the parenthesis term turns into zero, and multiplying by zero makes the whole thing zero.

This means that x values of 6 and 1 are solutions. But as you notice, x values of 6 and 1 appear in both answers B and C. You need to solve for the y values that go with those x values.

To get the y values, "plug" x = 6 into either equation and solve for y. And then repeat for x = 1. The ordered pairs that result are the places where the two lines/curves cross each other, and they are the solution to this system.

Answer 12

Hope this helps... take your time and read through it... feel free to ask any follow-up questions... this is important stuff in algebra, so if you don't "get it", let's figure out what you might be missing.

Answer 13

@JakeV8, Sorry for just ignoring you. Things came up and had to leave my computer. How do I plug in the values

Answer 14

Im thinking the answer is C

Answer 15

Do you understand all of the above? I almost recommend you copy/paste it into some sort of word doc or email or something for reference... :) t'is good notes for your class :)

Answer 16

Yes, I have wrote some down in my notebook

Answer 17

but yes... :) answer C looks right to me :)

Answer 18

Thanks for everything... And Im sorry again

Answer 19

hey, no problem :) Just do your best, and try to be generous to those who help you here... they like helping people who like to learn.... people "fishing" for answers get less attention!!

good luck!!