SOLUTION: y=-x+5 y=2x-4 Solve the following systems of equations using any method.

Algebra ->  Systems-of-equations -> SOLUTION: y=-x+5 y=2x-4 Solve the following systems of equations using any method.      Log On


   

Question 763789: y=-x+5
y=2x-4 Solve the following systems of equations
using any method.
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
y=-x+5
y=2x-4
-------------------
2x-4 = -x+5
3x = 9
x = 3
===================
Cheers,
Stan H.
===============

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

y=-x%2B5
y=2x-4
__________________
x%2By=5
-2x%2By=-4

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



Start with the given system of equations:


1x%2By=5

-2x%2By=-4





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


1x%2By=5 Start with the given equation



1y=5-x Subtract +x from both sides



1y=-x%2B5 Rearrange the equation



y=%28-x%2B5%29%2F%281%29 Divide both sides by 1



y=%28-1%2F1%29x%2B%285%29%2F%281%29 Break up the fraction



y=-x%2B5 Reduce



Now lets graph y=-x%2B5 (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%2B5%29+ Graph of y=-x%2B5




So let's solve for y on the second equation


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



1y=-4%2B2x Add 2+x to both sides



1y=%2B2x-4 Rearrange the equation



y=%28%2B2x-4%29%2F%281%29 Divide both sides by 1



y=%28%2B2%2F1%29x%2B%28-4%29%2F%281%29 Break up the fraction



y=2x-4 Reduce





Now lets add the graph of y=2x-4 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B5%2C2x-4%29+ Graph of y=-x%2B5(red) and y=2x-4(green)


From the graph, we can see that the two lines intersect at the point (3,2) (note: you might have to adjust the window to see the intersection)