SOLUTION: Find the x- and y-intercepts (if any) for each line. Show your work. Plot those intercepts, and graph the two lines on the same chart. Submit your graph through the Dropbox. Ap

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Find the x- and y-intercepts (if any) for each line. Show your work. Plot those intercepts, and graph the two lines on the same chart. Submit your graph through the Dropbox. Ap      Log On

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Question 263065: Find the x- and y-intercepts (if any) for each line. Show your work.
Plot those intercepts, and graph the two lines on the same chart. Submit your graph through the Dropbox.
Apply elimination or substitution to find the coordinates of the point of intersection (if there are no solutions or infinite solutions, state this). Show your work.
The 2 equations are:
x + 5y = 29
-7x + 4y = 70
Below is what I came up with but I just want to know if I did this correctly.
x + 5y = 29
y = 0 x + 5(0) = 29
x = 29
x = 0 0 + 5y = 29
5y = 29
y = 29/5
-7x + 4y = 70
y = 0 -7x + 4(0)= 70
-7x = 70
x = -10
x = 0 -7(0) + 4y = 70
4y = 70
y = 70/4 = 35/2

I will use the substitution system to point of intersection.
x = 29 - 5y
-7(29 - 5y) + 4y = 70
-203 + 35y + 4y = 70
39y = 273
y = 7
x + 5(7) = 29
x + 35 = 29
x = 29/35
Found 3 solutions by dabanfield, oberobic, checkley77:
Answer by dabanfield(803) About Me  (Show Source):
You can put this solution on YOUR website!
x + 35 = 29
x = 29/35
Very good except the last statement should be:
x = 29 - 35 = -6
:)

Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
x + 5y = 29
-7x + 4y = 70
.
x + 5y = 29
5y = -x +29
y = -1/5*x + 29/5
by inspection we can see that when
x = 0, y = 29/5
and when
y = 0, x = 29
.
-7x + 4y = 70
4y = 7x +70
y = 7/4*x + 70/4
again by inspection we can see that when
x = 0, y = 70/4
y = 0, x = -10
.
The two graphs are:
graph%28500%2C500%2C-30%2C40%2C-20%2C20%2C-1%2F5%2Ax%2B29%2F5%2C7%2F4%2Ax%2B70%2F4%29
.
Solving them as simultaneous equations, we have:
x + 5y = 29
-7x + 4y = 70
Multiplying the first equation by 7, we have:
7x + 35y = 203
-7x + 4y = 70
Adding
39y = 273
y = 273/39 = 7
Substituting in the first equation
x + 5(7) = 29
x = 29 - 35 = -6
.
so the point of intersection is: (-6, 7)
.
Done.

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!

The 2 equations are:
x + 5y = 29
-7x + 4y = 70
Below is what I came up with but I just want to know if I did this correctly.
x + 5y = 29
y = 0 x + 5(0) = 29
x = 29
x = 0 0 + 5y = 29
5y = 29
y = 29/5
-7x + 4y = 70
y = 0 -7x + 4(0)= 70
-7x = 70
x = -10
x = 0 -7(0) + 4y = 70
4y = 70
y = 70/4 = 35/2
I will use the substitution system to point of intersection.
x = 29 - 5y
-7(29 - 5y) + 4y = 70
-203 + 35y + 4y = 70
39y = 273
y = 7
x + 5(7) = 29
x + 35 = 29
x = 29/35 GOOD WORK UP TO THIS POINT [X=29-35=-6 ans.]
Check the graph below.
+graph%28+300%2C+200%2C+-8%2C+5%2C+-10%2C+10%2C+-x%2F5+%2B29%2F5+%2C+7x%2F4+%2B35%2F2%29+ (graph 300x200 pixels, x from -8 to 5, y from -10 to 10, of TWO functions -x/5 +29/5 and 7x/4 +35/2).