SOLUTION: Solve the following system of equations by graphing and select the correct answer below: 3x + 5y = 38 4x − 2y = 16

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve the following system of equations by graphing and select the correct answer below: 3x + 5y = 38 4x − 2y = 16      Log On


   

Question 976965: Solve the following system of equations by graphing and select the correct answer below:
3x + 5y = 38
4x − 2y = 16
Answer by MathLover1(20849) 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:


3x%2B5y=38

4x-2y=16





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%2B5y=38 Start with the given equation



5y=38-3x Subtract 3+x from both sides



5y=-3x%2B38 Rearrange the equation



y=%28-3x%2B38%29%2F%285%29 Divide both sides by 5



y=%28-3%2F5%29x%2B%2838%29%2F%285%29 Break up the fraction



y=%28-3%2F5%29x%2B38%2F5 Reduce



Now lets graph y=%28-3%2F5%29x%2B38%2F5 (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+%28-3%2F5%29x%2B38%2F5%29+ Graph of y=%28-3%2F5%29x%2B38%2F5




So let's solve for y on the second equation


4x-2y=16 Start with the given equation



-2y=16-4x Subtract 4+x from both sides



-2y=-4x%2B16 Rearrange the equation



y=%28-4x%2B16%29%2F%28-2%29 Divide both sides by -2



y=%28-4%2F-2%29x%2B%2816%29%2F%28-2%29 Break up the fraction



y=2x-8 Reduce





Now lets add the graph of y=2x-8 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-3%2F5%29x%2B38%2F5%2C2x-8%29+ Graph of y=%28-3%2F5%29x%2B38%2F5(red) and y=2x-8(green)


From the graph, we can see that the two lines intersect at the point (6,4) (note: you might have to adjust the window to see the intersection)