Question

Graph the two equations to solve the system.
3x + 2y = 6
y = -3/2 x - 1

Answer 1

find the intersection between these two graphs

Answer 2

Solve for y in the first equation first. Then graph and find the intersection as @higgs suggested.

Answer 3

First move 3x to the right side by using inverse operation (subtraction).

THEN get the y by itself through inverse operation (division)

Answer 4

If you don't have a graphing calculator:
http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

Enter the two functions on the first page, then click graph on the right. Afterwards, if you can't tell where the intersection is located, click on the tab at the top labelled INTERSECTION, put check marks in the boxes next to the functions...and I think the rest is self-explanatory.

Answer 5

ok

Answer 6

Let me know if you have a problem with it...

Answer 7

wait how do i find out where the intersection is again

Answer 8

it says there is no intersection

Answer 9

hahaha i figured it out

Answer 10

My fault!! I apologize for taking so long...glad you figured it out!! : )

Answer 11

So you got two parallel lines right? Just to clarify.

Answer 12

Parallel lines (lines that NEVER intersect) have the SAME slopes but DIFFERENT y-intercepts.

Answer 13

Which is the case for this particular problem.

Answer 14

no sorry i got stuck again! and its irritating me!

Answer 15

Same problem or a new one? Sorry I was in the computer science forum.

Answer 16

same problem but is it -5,14

Answer 17

-14

Answer 18

Cool...let's look at the first equation again...

Answer 19

3x + 2y = 6

Answer 20

We want to solve for y (i.e. get y alone)

Answer 21

So we start by moving 3x to the right side of the equal sign. But we can only do that by using inverse (opposite) operations.
Inverse operation: Since it's positive 3x (+3x), we move it using negative 3x (-3x)

Answer 22

3x + 2y = 6
-3x + 2y = -3x + 6
-------------------
0x + 2y = -3x + 6

2y = -3x + 6

Now we need to get the y by itself, again by using inverse (opposite) operation.
Inverse operation: Since it's 2y (2 times y) and we want y alone, we need to divide (2y/2).

2y/2 = -3x/2 + 6/2

Simplifies too...

Answer 23

to*...

Answer 24

y = -3/2x + 3

Answer 25

The 2s on the left cancel each other out. And 6/2 = 3 on the far right.

The fraction next to x stays as it is.

Answer 26

ok

Answer 27

The 2nd equation is:
y = -3/2x -1

Answer 28

They BOTH share the SAME slope, but have DIFFERENT y-intercepts (one y-interecept is 3, the other y-intercept is -1)

Answer 29

That's a math rule:
PARALLEL (//) lines and equations, have the EXACT SAME slope but different y-intercepts.

Answer 30

// = parallel, btw.

Answer 31

So these two equations:
y = -3/2x + 3
and
y = -3/2x - 1

will NEVER intersect. Therefore there is: No Solution.

Answer 32

ok

Answer 33

Or an empty set: \[{\emptyset}\]

Answer 34

Good job. Take care

Answer 35

thanks

Answer 36

No problem. Don't forget to select a Best Response. Take care