SOLUTION: HELP, I think the answer is x=7 and y=7 but how do you set this up. Use elimination to solve each system of equations. 4X-2Y=14 Y=X

Question 183033: HELP, I think the answer is x=7 and y=7 but how do you set this up. Use elimination to solve each system of equations. 4X-2Y=14 Y=X
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the second equation.

Subtract "x" from both sides (the goal is to get all the variable terms to the left side).

So we have the system of equations:

Multiply the both sides of the second equation by 2.

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.

Divide both sides by to isolate .

Reduce.

So our answer is and (so you are correct).

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)

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