SOLUTION: Please help: Find the values of x and y that solve the following system of equations: 4x-7y = 4 5x+2y = 5

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Question 299407: Please help: Find the values of x and y that solve the following system of equations:
4x-7y = 4
5x+2y = 5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%284x-7y=4%2C5x%2B2y=5%29


2%284x-7y%29=2%284%29 Multiply the both sides of the first equation by 2.


8x-14y=8 Distribute and multiply.


7%285x%2B2y%29=7%285%29 Multiply the both sides of the second equation by 7.


35x%2B14y=35 Distribute and multiply.


So we have the new system of equations:
system%288x-14y=8%2C35x%2B14y=35%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%288x-14y%29%2B%2835x%2B14y%29=%288%29%2B%2835%29


%288x%2B35x%29%2B%28-14y%2B14y%29=8%2B35 Group like terms.


43x%2B0y=43 Combine like terms.


43x=43 Simplify.


x=%2843%29%2F%2843%29 Divide both sides by 43 to isolate x.


x=1 Reduce.


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8x-14y=8 Now go back to the first equation.


8%281%29-14y=8 Plug in x=1.


8-14y=8 Multiply.


-14y=8-8 Subtract 8 from both sides.


-14y=0 Combine like terms on the right side.


y=%280%29%2F%28-14%29 Divide both sides by -14 to isolate y.


y=0 Reduce.


So the solutions are x=1 and y=0.


Which form the ordered pair .


This means that the system is consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of 4x-7y=4 (red) and 5x%2B2y=5 (green)