SOLUTION: Which is the solution to this pair of linear equations? 5y-2x=6 3x-2y=13

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Question 401487: Which is the solution to this pair of linear equations?
5y-2x=6
3x-2y=13
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

5y-2x=6
3x-2y=13

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



Start with the given system of equations:


-2x%2B5y=6

3x-2y=13





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


-2x%2B5y=6 Start with the given equation



5y=6%2B2x Add 2+x to both sides



5y=%2B2x%2B6 Rearrange the equation



y=%28%2B2x%2B6%29%2F%285%29 Divide both sides by 5



y=%28%2B2%2F5%29x%2B%286%29%2F%285%29 Break up the fraction



y=%282%2F5%29x%2B6%2F5 Reduce



Now lets graph y=%282%2F5%29x%2B6%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+%282%2F5%29x%2B6%2F5%29+ Graph of y=%282%2F5%29x%2B6%2F5




So let's solve for y on the second equation


3x-2y=13 Start with the given equation



-2y=13-3x Subtract 3+x from both sides



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



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



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



y=%283%2F2%29x-13%2F2 Reduce





Now lets add the graph of y=%283%2F2%29x-13%2F2 to our first plot to get:


Graph of y=%282%2F5%29x%2B6%2F5(red) and y=%283%2F2%29x-13%2F2(green)


From the graph, we can see that the two lines intersect at the point (7,4) (note: you might have to adjust the window to see the intersection)