Graph doesn't match intercepts!

[justan4cat]

This is a lengthy problem, and I will show my work as I go. I will attach the graph, hopefully someone can see what I've done wrong because I have two of these to complete.

Find the x and y intercepts for each line.
4y+x=8
Y intercept: X intercept:
4y+0=8 4(0)+x=8
4y=8 x=8
Y=2 (8,0)
(0,2)

X=2y+7 First, I re-wrote it as: -2y+x=7
Y intercept: X intercept:
-2y=7 -2(0)+x=7
Y=-7/2 x=7
(0,-7/2) (7,0)

Apply elimination or substitution to find the coordinate of the point of intersection.
Substitution Method:
X=2y+7
4y+(2y+7)=8
6y+7=8
6y=1
Y=1/6

X=2(1/6)+7
X=9 1/6

The point of intersection coordinates should be (9 1/6, 1/6).

The "9" part isn't even near the lines. Something has to be wrong.

 

[pitoten]

X=2(1/6)+7
X=9 1/6.

check your algebra step one more time

 

[justan4cat]

I think the problem was with the substitution. It should have been:

4y+x=8
x=2y+7

4y+(2y+7)=8
6y+7=8
6y=1
y=1/6
Then,
x=2y+7
x=2(1/6)+7
x=2/6+7
x=7 1/3!!! It matches my graph now.

(7 1/3, 1/6)

 

[pitoten]

There you go. It is a common mistake that can happen while doing algebra. X*(Y/Z) does not equal the mixed fraction X y/z

 

[justan4cat]

I don't know what I'd do without you guys. Thanks!