SOLUTION: Find the common solution. 3x + 2y = 4 2x - y = 5

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Question 463182: Find the common solution.
3x + 2y = 4
2x - y = 5

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:


3x%2B2y=4

2x-y=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%2B2y=4 Start with the given equation



2y=4-3x Subtract 3+x from both sides



2y=-3x%2B4 Rearrange the equation



y=%28-3x%2B4%29%2F%282%29 Divide both sides by 2



y=%28-3%2F2%29x%2B%284%29%2F%282%29 Break up the fraction



y=%28-3%2F2%29x%2B2 Reduce



Now lets graph y=%28-3%2F2%29x%2B2 (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%2F2%29x%2B2%29+ Graph of y=%28-3%2F2%29x%2B2




So let's solve for y on the second equation


2x-y=5 Start with the given equation



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



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



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



y=%28-2%2F-1%29x%2B%285%29%2F%28-1%29 Break up the fraction



y=2x-5 Reduce





Now lets add the graph of y=2x-5 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-3%2F2%29x%2B2%2C2x-5%29+ Graph of y=%28-3%2F2%29x%2B2(red) and y=2x-5(green)


From the graph, we can see that the two lines intersect at the point (2,-1) (note: you might have to adjust the window to see the intersection)