SOLUTION: I just can't seem to grasph how to figure x & y. Please help!!! -4x + 3y = 10 5x - 7y = -32 5x =75 -2x -5y = 50

Algebra ->  Distributive-associative-commutative-properties -> SOLUTION: I just can't seem to grasph how to figure x & y. Please help!!! -4x + 3y = 10 5x - 7y = -32 5x =75 -2x -5y = 50      Log On


   

Question 148001: I just can't seem to grasph how to figure x & y. Please help!!!
-4x + 3y = 10
5x - 7y = -32
5x =75
-2x -5y = 50
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started


# 1



Start with the given system of equations:


system%28-4x+%2B+3y+=+10%2C5x+-+7y+=+-32%29


-4x+%2B+3y+=+10 Start with the first equation.


3y=10%2B4x Add 4x to both sides.


y=%2810%2B4x%29%2F%283%29 Divide both sides by 3 to isolate y.


y=%284%2F3%29x%2B10%2F3 Simplify.


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5x+-+7%28%284%2F3%29x%2B10%2F3%29+=+-32 Now plug in y=%284%2F3%29x%2B10%2F3 into the second equation.


5x-%2828%2F3%29x-70%2F3=-32 Multiply.


3%285x-%2828%2Fcross%283%29%29x-70%2Fcross%283%29%29=3%28-32%29 Multiply both sides by the LCD 3 to clear any fractions.


15x-28x-70=-96 Distribute and multiply.


-13x-70=-96 Combine like terms on the left side.


-13x=-96%2B70 Add 70 to both sides.


-13x=-26 Combine like terms on the right side.


x=%28-26%29%2F%28-13%29 Divide both sides by -13 to isolate x.


x=2 Reduce.


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Since we know that x=2, we can use this to find y.


-4x+%2B+3y+=+10 Go back to the first equation.


-4%282%29+%2B+3y+=+10 Plug in x=2.


-8%2B3y=10 Multiply.


3y=10%2B8 Add 8 to both sides.


3y=18 Combine like terms on the right side.


y=%2818%29%2F%283%29 Divide both sides by 3 to isolate y.


y=6 Reduce.


So the answer is x=2 and y=6.


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%2B3y=10 (red) and 5x-7y=-32 (green)