SOLUTION: May I have help with this problem? Solve the system by graphing: 5x + 4y =16 x- 2y =6

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Question 1007822: May I have help with this problem?
Solve the system by graphing:
5x + 4y =16
x- 2y =6

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

5x+%2B+4y+=16
x-+2y+=6
--------------------
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


5x%2B4y=16

1x-2y=6





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


5x%2B4y=16 Start with the given equation



4y=16-5x Subtract 5+x from both sides



4y=-5x%2B16 Rearrange the equation



y=%28-5x%2B16%29%2F%284%29 Divide both sides by 4



y=%28-5%2F4%29x%2B%2816%29%2F%284%29 Break up the fraction



y=%28-5%2F4%29x%2B4 Reduce



Now lets graph y=%28-5%2F4%29x%2B4 (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+%28-5%2F4%29x%2B4%29+ Graph of y=%28-5%2F4%29x%2B4




So let's solve for y on the second equation


1x-2y=6 Start with the given equation



-2y=6-x Subtract +x from both sides



-2y=-x%2B6 Rearrange the equation



y=%28-x%2B6%29%2F%28-2%29 Divide both sides by -2



y=%28-1%2F-2%29x%2B%286%29%2F%28-2%29 Break up the fraction



y=%281%2F2%29x-3 Reduce





Now lets add the graph of y=%281%2F2%29x-3 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-5%2F4%29x%2B4%2C%281%2F2%29x-3%29+ Graph of y=%28-5%2F4%29x%2B4(red) and y=%281%2F2%29x-3(green)


From the graph, we can see that the two lines intersect at the point (4,-1) (note: you might have to adjust the window to see the intersection)