SOLUTION: Solve the simultanous equation graphically x + y = 5 3x + y = 9

Algebra ->  Linear-equations -> SOLUTION: Solve the simultanous equation graphically x + y = 5 3x + y = 9      Log On


   

Question 1128889: Solve the simultanous equation graphically
x + y = 5
3x + y = 9
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

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



Start with the given system of equations:


1x%2By=5

3x%2By=9





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


3x%2By=9 Start with the given equation



1y=9-3x Subtract 3+x from both sides



1y=-3x%2B9 Rearrange the equation



y=%28-3x%2B9%29%2F%281%29 Divide both sides by 1



y=%28-3%2F1%29x%2B%289%29%2F%281%29 Break up the fraction



y=-3x%2B9 Reduce





Now lets add the graph of y=-3x%2B9 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B5%2C-3x%2B9%29+ Graph of y=-x%2B5(red) and y=-3x%2B9(green)


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