Question

Can someone please explain how to work these problems?

Which graph represents the solution?
1. y= -x+2
y=3x-1

Answer 1

id find the solution and see what quadrant its in ....

Answer 2

y= -x+2
y=3x-1

since y = y ...

-x+2 = 3x-1 .. solve for x

Answer 3

once you know a value for x, plug it into either equation to find y

Answer 4

What? I am not following you.

Answer 5

do you agree that if: n = a, and n = b ; then a = b?

Answer 6

Yes.

Answer 7

well, we have stated here that:

y = a and y = b , therefore a has to be equal to b they just gave equations instead ...

y= -x+2
y= 3x-1

therefore

-x+2 = 3x-1

this should be easily solvable for x now

Answer 8

But how do I solve it?

Answer 9

do you agree that if something is balanced; that in order to keep it balanced, you have to do the same thing to each side?

for example:

we know that 5 = 5 its balanced; to modify it, and keep it in balance, we would have to do the exact same thing to each side

5 = 5

5 - 2 = 5 - 2

(5-2)/7 = (5-2)/7

(5-2)/7 + x = (5-2)/7 + x

do you agree that this has remained balanced thruout?

Answer 10

Yes.

Answer 11

Would that be how to solve the problem, or no?

Answer 12

then lets apply this principle to the balanced equations for our problem

-x+2 = 3x - 1 ; lets add x to each side
+x +x
------------
0 + 2 = 4x - 1

what would you suggest we do next? keep in mind that we want x all alone

Answer 13

Simplify, 0+2 = 4x - 1.

Answer 14

ok

2 = 4x - 1

and next?

Answer 15

I don't know, ha. Ummm.. substitute?

Answer 16

lets work at getting rid of the -1 on the right ... i say we add 1, since -1+1 = 0

2 = 4x - 1 ; add 1 to each side
+1 +1
-----------
3 = 4x

now we are one step away .... what would you suggest we do now?

Answer 17

Multiply 4 by itself, i don't know..

Answer 18

close, recall that anything DIVIDED BY itself is equal to 1, except 0/0

so, 4/4 = 1 , lets divide both sides by 4

3 = 4x ; divide by 4
/4 /4
-------
3/4 = x

and since they have decimal values on the graphs, x = .75

how many graphs have a crossing at x = .75?

Answer 19

The first one, has .75.

Answer 20

i agree, none of the others fit x = .75 so id go with that one :)

Answer 21

Thanks, for explaining this step by step with me I appreciate it. I'll give you a medal for best answer.

Answer 22

youre welcome, and good luck ;)

Answer 23

Thanks.