SOLUTION: Identify the solution(s) of the system of equations, if any. 4x + 4y = 4 y = 5 - 5x

Algebra ->  Graphs -> SOLUTION: Identify the solution(s) of the system of equations, if any. 4x + 4y = 4 y = 5 - 5x       Log On


   

Question 973055: Identify the solution(s) of the system of equations, if any.
4x + 4y = 4
y = 5 - 5x
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

4x+%2B+4y+=+4
y+=+5+-+5x
----------------------------
4x+%2B+4y+=+4
5x%2By+=+5+
------------------
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


4x%2B4y=4

5x%2By=5





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


4x%2B4y=4 Start with the given equation



4y=4-4x Subtract 4+x from both sides



4y=-4x%2B4 Rearrange the equation



y=%28-4x%2B4%29%2F%284%29 Divide both sides by 4



y=%28-4%2F4%29x%2B%284%29%2F%284%29 Break up the fraction



y=-x%2B1 Reduce



Now lets graph y=-x%2B1 (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%2B1%29+ Graph of y=-x%2B1




So let's solve for y on the second equation


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



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



1y=-5x%2B5 Rearrange the equation



y=%28-5x%2B5%29%2F%281%29 Divide both sides by 1



y=%28-5%2F1%29x%2B%285%29%2F%281%29 Break up the fraction



y=-5x%2B5 Reduce





Now lets add the graph of y=-5x%2B5 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B1%2C-5x%2B5%29+ Graph of y=-x%2B1(red) and y=-5x%2B5(green)


From the graph, we can see that the two lines intersect at the point (1,0) (note: you might have to adjust the window to see the intersection)