SOLUTION: Use the substitution method to solve the linear system. y = x - 4 3x - y = -8 I need help graphing the equations. Thank you, Shannon

Algebra ->  Linear-equations -> SOLUTION: Use the substitution method to solve the linear system. y = x - 4 3x - y = -8 I need help graphing the equations. Thank you, Shannon      Log On


   

Question 394281: Use the substitution method to solve the linear system.
y = x - 4
3x - y = -8
I need help graphing the equations.
Thank you,
Shannon
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

y+=+x+-+4...write in standard form
3x+-+y+=+-8
----------------
-x+%2B+y+=++-+4
3x+-+y+=+-8
--------------------
Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++-1%5Cx+%2B+1%5Cy+=+-4%2C%0D%0A++++3%5Cx+%2B+-1%5Cy+=+-8+%29%0D%0A++We'll use substitution. After moving 1*y to the right, we get:
-1%2Ax+=+-4+-+1%2Ay, or x+=+-4%2F-1+-+1%2Ay%2F-1. Substitute that
into another equation:
3%2A%28-4%2F-1+-+1%2Ay%2F-1%29+%2B+-1%5Cy+=+-8 and simplify: So, we know that y=-10. Since x+=+-4%2F-1+-+1%2Ay%2F-1, x=-6.

Answer: system%28+x=-6%2C+y=-10+%29.



now graph:

Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


-x%2By=-4

3x-y=-8





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


-x%2By=-4 Start with the given equation



1y=-4%2Bx Add +x to both sides



1y=%2Bx-4 Rearrange the equation



y=%28%2Bx-4%29%2F%281%29 Divide both sides by 1



y=%28%2B1%2F1%29x%2B%28-4%29%2F%281%29 Break up the fraction



y=x-4 Reduce



Now lets graph y=x-4 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x-4%29+ Graph of y=x-4




So let's solve for y on the second equation


3x-y=-8 Start with the given equation



-y=-8-3x Subtract 3+x from both sides



-y=-3x-8 Rearrange the equation



y=%28-3x-8%29%2F%28-1%29 Divide both sides by -1



y=%28-3%2F-1%29x%2B%28-8%29%2F%28-1%29 Break up the fraction



y=3x%2B8 Reduce





Now lets add the graph of y=3x%2B8 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x-4%2C3x%2B8%29+ Graph of y=x-4(red) and y=3x%2B8(green)


From the graph, we can see that the two lines intersect at the point (-6,-10) (note: you might have to adjust the window to see the intersection)