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

Question 202454: x-4y=29
x-y=5
Found 2 solutions by jim_thompson5910, rfer:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:

Multiply the both sides of the second equation by -1.

Distribute and multiply.

So we have the new system of equations:

Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:

Group like terms.

Combine like terms.

Simplify.

Divide both sides by to isolate .

Reduce.

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

Now go back to the first equation.

Plug in .

Multiply.

Subtract from both sides.

Combine like terms on the right side.

So the solutions are and .

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 (red) and (green)

Answer by rfer(16322) (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
----------
check
-3-4(-8)=29
-3=32=29
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