SOLUTION: Solve by the addition method? 6x - y = 49 x + 6y = 39 What is the solution of the system? (Simplify you answer. Type an order pair?)

Question 157504: Solve by the addition method?
6x - y = 49
x + 6y = 39
What is the solution of the system?
(Simplify you answer. Type an order pair?)
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 -6.

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. Notice how the x terms cancel out.

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 our answer is 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)

Questions? Email me at jim_thompson5910@hotmail.com
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