SOLUTION: Solve each system by graphing 3x-4y=13 2x+y=5 I got y=2x-5 and y=3/4-13/4 Is that correct? If not can you please show me how to get the correct answer? Please show me how to gra

Algebra ->  Graphs -> SOLUTION: Solve each system by graphing 3x-4y=13 2x+y=5 I got y=2x-5 and y=3/4-13/4 Is that correct? If not can you please show me how to get the correct answer? Please show me how to gra      Log On


   



Question 906646: Solve each system by graphing
3x-4y=13
2x+y=5
I got y=2x-5 and y=3/4-13/4 Is that correct? If not can you please show me how to get the correct answer? Please show me how to graph it too! Thank you.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

3x-4y=13...eq.1
2x%2By=5.....eq.2
___________________

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



Start with the given system of equations:


3x-4y=13

2x%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


3x-4y=13 Start with the given equation



-4y=13-3x Subtract 3+x from both sides



-4y=-3x%2B13 Rearrange the equation



y=%28-3x%2B13%29%2F%28-4%29 Divide both sides by -4



y=%28-3%2F-4%29x%2B%2813%29%2F%28-4%29 Break up the fraction



y=%283%2F4%29x-13%2F4 Reduce



Now lets graph y=%283%2F4%29x-13%2F4 (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+%283%2F4%29x-13%2F4%29+ Graph of y=%283%2F4%29x-13%2F4




So let's solve for y on the second equation


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



1y=5-2x Subtract 2+x from both sides



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



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



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



y=-2x%2B5 Reduce





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


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%283%2F4%29x-13%2F4%2C-2x%2B5%29+ Graph of y=%283%2F4%29x-13%2F4(red) and y=-2x%2B5(green)


From the graph, we can see that the two lines intersect at the point (3,-1) (note: you might have to adjust the window to see the intersection)