SOLUTION: I have gotten thru 4 of the 8 questions on my worksheet and am stuck with this one. the direction say to "solve each system by elimination" 12x

SOLUTION: I have gotten thru 4 of the 8 questions on my worksheet and am stuck with this one. the direction say to "solve each system by elimination" 12x - 7y = -10 -4x + 3y = 10 I

Question 198012: I have gotten thru 4 of the 8 questions on my worksheet and am stuck with this one. the direction say to "solve each system by elimination"
12x - 7y = -10
-4x + 3y = 10
I can't seem to get either side to cancel out.
Found 2 solutions by jim_thompson5910, josmiceli:
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 3.

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.

Add to both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

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 josmiceli(19441) (Show Source): You can put this solution on YOUR website!

Multiply both sides of the 2nd equation by
and add the equations

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

Plug this result back in to 2nd equation

The solution is ,
check:

and

OK
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