SOLUTION: 4x + 5y =40 6x + 7y =58 the same variable will satifty the solution

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Question 179497: 4x + 5y =40
6x + 7y =58


the same variable will satifty the solution
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%2B5y=40%2C6x%2B7y=58%29


3%284x%2B5y%29=3%2840%29 Multiply the both sides of the first equation by 3.


12x%2B15y=120 Distribute and multiply.


-2%286x%2B7y%29=-2%2858%29 Multiply the both sides of the second equation by -2.


-12x-14y=-116 Distribute and multiply.


So we have the new system of equations:
system%2812x%2B15y=120%2C-12x-14y=-116%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:


%2812x%2B15y%29%2B%28-12x-14y%29=%28120%29%2B%28-116%29


%2812x%2B-12x%29%2B%2815y%2B-14y%29=120%2B-116 Group like terms.


0x%2By=4 Combine like terms.


y=4 Simplify.


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12x%2B15y=120 Now go back to the first equation.


12x%2B15%284%29=120 Plug in y=4.


12x%2B60=120 Multiply.


12x=120-60 Subtract 60 from both sides.


12x=60 Combine like terms on the right side.


x=%2860%29%2F%2812%29 Divide both sides by 12 to isolate x.


x=5 Reduce.


So our answer is x=5 and y=4.


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%2B5y=40 (red) and 6x%2B7y=58 (green)