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

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

2x%2B%282%2F3%29y+=4 Start with the first equation.


3%282x%29%2Bcross%283%29%28%282%2Fcross%283%29%29y%29=3%284%29 Multiply EVERY term by the LCD 3 to clear any fractions.


6x%2B2y=12 Distribute and multiply.

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x-%281%2F2%29y=7 Move onto the second equation.


2%28x%29-cross%282%29%28%281%2Fcross%282%29%29y%29=2%287%29 Multiply EVERY term by the LCD 2 to clear any fractions.


2x-y=14 Distribute and multiply.


So we have the system of equations:


system%286x%2B2y=12%2C2x-y=14%29




2%282x-y%29=2%2814%29 Multiply the both sides of the second equation by 2.


4x-2y=28 Distribute and multiply.


So we have the new system of equations:
system%286x%2B2y=12%2C4x-2y=28%29


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


%286x%2B2y%29%2B%284x-2y%29=%2812%29%2B%2828%29


%286x%2B4x%29%2B%282y%2B-2y%29=12%2B28 Group like terms.


10x%2B0y=40 Combine like terms.


10x=40 Simplify.


x=%2840%29%2F%2810%29 Divide both sides by 10 to isolate x.


x=4 Reduce.


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6x%2B2y=12 Now go back to the first equation.


6%284%29%2B2y=12 Plug in x=4.


24%2B2y=12 Multiply.


2y=12-24 Subtract 24 from both sides.


2y=-12 Combine like terms on the right side.


y=%28-12%29%2F%282%29 Divide both sides by 2 to isolate y.


y=-6 Reduce.


So our answer is x=4 and y=-6.


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 6x%2B2y=12 (red) and 2x-y=14 (green)