SOLUTION: 5y-3x=1 4y+2x=80

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Question 202188: 5y-3x=1
4y+2x=80
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%28-3x%2B5y=1%2C2x%2B4y=80%29


-3x%2B5y=1 Start with the first equation.


5y=1%2B3x Add 3x to both sides.


y=%281%2B3x%29%2F%285%29 Divide both sides by 5 to isolate y.


y=%283%2F5%29x%2B1%2F5 Rearrange the terms and simplify.


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2x%2B4y=80 Move onto the second equation.


2x%2B4%28%283%2F5%29x%2B1%2F5%29=80 Now plug in y=%283%2F5%29x%2B1%2F5.


2x%2B%2812%2F5%29x%2B4%2F5=80 Distribute.


5%282x%2B%2812%2Fcross%285%29%29x%2B4%2Fcross%285%29%29=5%2880%29 Multiply both sides by the LCD 5 to clear any fractions.


10x%2B12x%2B4=400 Distribute and multiply.


22x%2B4=400 Combine like terms on the left side.


22x=400-4 Subtract 4 from both sides.


22x=396 Combine like terms on the right side.


x=%28396%29%2F%2822%29 Divide both sides by 22 to isolate x.


x=18 Reduce.


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Since we know that x=18, we can use this to find y.


-3x%2B5y=1 Go back to the first equation.


-3%2818%29%2B5y=1 Plug in x=18.


-54%2B5y=1 Multiply.


5y=1%2B54 Add 54 to both sides.


5y=55 Combine like terms on the right side.


y=%2855%29%2F%285%29 Divide both sides by 5 to isolate y.


y=11 Reduce.


So the solutions are x=18 and y=11.


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 -3x%2B5y=1 (red) and 2x%2B4y=80 (green)