SOLUTION: 5x+4y=7 x-3y=9

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Question 146564: 5x+4y=7
x-3y=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:


5x%2B4y=7

1x-3y=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


5x%2B4y=7 Start with the given equation



4y=7-5x Subtract 5+x from both sides



4y=-5x%2B7 Rearrange the equation



y=%28-5x%2B7%29%2F%284%29 Divide both sides by 4



y=%28-5%2F4%29x%2B%287%29%2F%284%29 Break up the fraction



y=%28-5%2F4%29x%2B7%2F4 Reduce



Now lets graph y=%28-5%2F4%29x%2B7%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+%28-5%2F4%29x%2B7%2F4%29+ Graph of y=%28-5%2F4%29x%2B7%2F4




So let's solve for y on the second equation


1x-3y=9 Start with the given equation



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



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



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



y=%28-1%2F-3%29x%2B%289%29%2F%28-3%29 Break up the fraction



y=%281%2F3%29x-3 Reduce





Now lets add the graph of y=%281%2F3%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%2B7%2F4%2C%281%2F3%29x-3%29+ Graph of y=%28-5%2F4%29x%2B7%2F4(red) and y=%281%2F3%29x-3(green)


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