SOLUTION: x-4y=29 x-y=5

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Question 202454: x-4y=29
x-y=5
Found 2 solutions by jim_thompson5910, rfer:
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%28x-4y=29%2Cx-y=5%29


-1%28x-y%29=-1%285%29 Multiply the both sides of the second equation by -1.


-x%2By=-5 Distribute and multiply.


So we have the new system of equations:
system%28x-4y=29%2C-x%2By=-5%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:


%28x-4y%29%2B%28-x%2By%29=%2829%29%2B%28-5%29


%28x-x%29%2B%28-4y%2By%29=29%2B-5 Group like terms.


0x-3y=24 Combine like terms.


-3y=24 Simplify.


y=%2824%29%2F%28-3%29 Divide both sides by -3 to isolate y.


y=-8 Reduce.


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x-4y=29 Now go back to the first equation.


x-4%28-8%29=29 Plug in y=-8.


x%2B32=29 Multiply.


x=29-32 Subtract 32 from both sides.


x=-3 Combine like terms on the right side.


So the solutions are x=-3 and y=-8.


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 x-4y=29 (red) and x-y=5 (green)

Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
x-4y=29
x-y=5
x=y+5
------------
y+5-4y=29
-3y=24
y=-8
-----------
x-(-8)=5
x=-3
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check
-3-4(-8)=29
-3=32=29