SOLUTION: HELP. Use elimination to solve each system of equations. 2X+2/3Y =4 X-1/2Y=7

Question 183031: HELP. Use elimination to solve each system of equations. 2X+2/3Y =4 X-1/2Y=7
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the first equation.

Multiply EVERY term by the LCD to clear any fractions.

Distribute and multiply.

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

Move onto the second equation.

Multiply EVERY term by the LCD to clear any fractions.

Distribute and multiply.

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 .

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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