SOLUTION: Solve the system of eqations. 7x + 24y = 24 3x - 4y = -4

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Question 241414: Solve the system of eqations.
7x + 24y = 24
3x - 4y = -4
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%287x%2B24y=24%2C3x-4y=-4%29


6%283x-4y%29=6%28-4%29 Multiply the both sides of the second equation by 6.


18x-24y=-24 Distribute and multiply.


So we have the new system of equations:
system%287x%2B24y=24%2C18x-24y=-24%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:


%287x%2B24y%29%2B%2818x-24y%29=%2824%29%2B%28-24%29


%287x%2B18x%29%2B%2824y%2B-24y%29=24%2B-24 Group like terms.


25x%2B0y=0 Combine like terms.


25x=0 Simplify.


x=%280%29%2F%2825%29 Divide both sides by 25 to isolate x.


x=0 Reduce.


------------------------------------------------------------------


7x%2B24y=24 Now go back to the first equation.


7%280%29%2B24y=24 Plug in x=0.


0%2B24y=24 Multiply.


24y=24-0 Subtract 0 from both sides.


24y=24 Combine like terms on the right side.


y=%2824%29%2F%2824%29 Divide both sides by 24 to isolate y.


y=1 Reduce.


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


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 7x%2B24y=24 (red) and 3x-4y=-4 (green)