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

Algebra ->  Coordinate Systems and Linear Equations -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

y=x Start with the second equation.


-x%2By=0 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:
system%284x-2y=14%2C-x%2By=0%29


2%28-x%2By%29=2%280%29 Multiply the both sides of the second equation by 2.


-2x%2B2y=0 Distribute and multiply.


So we have the new system of equations:
system%284x-2y=14%2C-2x%2B2y=0%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:


%284x-2y%29%2B%28-2x%2B2y%29=%2814%29%2B%280%29


%284x%2B-2x%29%2B%28-2y%2B2y%29=14%2B0 Group like terms.


2x%2B0y=14 Combine like terms.


2x=14 Simplify.


x=%2814%29%2F%282%29 Divide both sides by 2 to isolate x.


x=7 Reduce.


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4x-2y=14 Now go back to the first equation.


4%287%29-2y=14 Plug in x=7.


28-2y=14 Multiply.


-2y=14-28 Subtract 28 from both sides.


-2y=-14 Combine like terms on the right side.


y=%28-14%29%2F%28-2%29 Divide both sides by -2 to isolate y.


y=7 Reduce.


So our answer is x=7 and y=7 (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 4x-2y=14 (red) and y=x (green)