Solving Systems of Equations by Substitution

A

audvor16

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Feb 21, 2013
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I'm having trouble trying to even do the right work. I'm very confused on which equation I should start with or if it matter. Everytime I feel like I did it right, I look in the back of the book (which has the answers) and I get it wrong. HELP!!!IM SO FRUSTRATED! Then it's also asking to graph after I solve it.

2x-y=-3
x+y=9

Here's what I did:
-y=-2x-3
div. by -1

y=2x+3
then

x+(2x+3)=9
3x+3=9
-3
div. by 3
x=2
......

y=2(2)+3
y=4+3=7

(2,7)

WOW ok so turns out I just got that one right.....haha..ha:grin:
but now I need to know how to plot the graphs of the two equations! By this do they mean the 2 equations that I started with? or the equations that I... simplified(idk if i used the right term. hopefully you know what I mean.)
 
audvor16 said:
I'm having trouble trying to even do the right work. I'm very confused on which equation I should start with or if it matter. Everytime I feel like I did it right, I look in the back of the book (which has the answers) and I get it wrong. HELP!!!IM SO FRUSTRATED! Then it's also asking to graph after I solve it.

2x-y=-3
x+y=9

Here's what I did:
-y=-2x-3
div. by -1

y=2x+3
then

x+(2x+3)=9
3x+3=9
-3
div. by 3
x=2
......

y=2(2)+3
y=4+3=7

(2,7)

WOW ok so turns out I just got that one right.....haha..ha:grin:
but now I need to know how to plot the graphs of the two equations! By this do they mean the 2 equations that I started with? or the equations that I... simplified(idk if i used the right term. hopefully you know what I mean.)
Click to expand...

Yes ... graph the equations you started with. Namely:

2x-y=-3
x+y=9

By the way, you should check your work by substituting the values in the equation. For example:

2x - y = 2*2 - 7 = -3 ........................checks

2 + 7 = 9 .........................................checks
 
Okay, so I should make both equations equal Y?

soooooo

y=2x+3
y=9-x

then
..............................x................................................... y=2x+3......................
1
5
27
39

..............................x........................................................ y=9-x.....................
1
8
27
36
 
Last edited:
audvor16 said:
Okay, so I should make both equations equal Y?

soooooo

y=2x+3
y=9-x

then
..............................x................................................... y=2x+3......................
15
27
39

..............................x........................................................ y=9-x.....................
18
27
36
Click to expand...

Looks good - now plot those.....
 
A "linear equation" is so called because its graph is a straight line. And a straight line is determined by two points. You could, for example, have noted that, in 2x- y= -3, if x= 0 we have -y= -3 or y= 3 so one point is (0, 3) and, if y= 0, 2x= -3 so x= -3/2. Another point is (-3/2, 0). Mark those two points and draw the unique line through them. Of course, a third point, as a check, is not a bad idea.
 
audvor16 said:
Here's what I did:

-y=-2x-3

div. by -1 . . . This isn't stated correctly. You should get credit for this if you type something such as
"Divide each side by -1."

y=2x+3

then

x+(2x+3)=9

3x+3=9

-3 . . . The same of comment above applies here a second time. Try "Subtract 3 from each side." Or, "Add -3 to each side."


div. by 3 . . . It's the same again for a third time. Try "Divide each side by -3."

x=2
......
Click to expand...

Saying or thinking something aloud isn't necessarily going to translate to correctly written steps.
You want to maximize your chances of receiving the highest number of points on a problem.


Regarding your work, I could come back with:

Divide what by -1?

Subtract 3 from what?

Divide what by 3?
 
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