SOLUTION: Please help me. I have tried to get this for the past hour and a half. I give up. 2x+7y=22 -4x+9y=2 Find x and y and graph. Tyvm, judy

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Please help me. I have tried to get this for the past hour and a half. I give up. 2x+7y=22 -4x+9y=2 Find x and y and graph. Tyvm, judy      Log On


   

Question 173318: Please help me. I have tried to get this for the past hour and a half. I give up.
2x+7y=22
-4x+9y=2
Find x and y and graph. Tyvm, judy
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%282x%2B7y=22%2C-4x%2B9y=2%29


2%282x%2B7y%29=2%2822%29 Multiply the both sides of the first equation by 2.


4x%2B14y=44 Distribute and multiply.


So we have the new system of equations:
system%284x%2B14y=44%2C-4x%2B9y=2%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%2B14y%29%2B%28-4x%2B9y%29=%2844%29%2B%282%29


%284x%2B-4x%29%2B%2814y%2B9y%29=44%2B2 Group like terms.


0x%2B23y=46 Combine like terms. Notice how the x terms cancel out.


23y=46 Simplify.


y=%2846%29%2F%2823%29 Divide both sides by 23 to isolate y.


y=2 Reduce.


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


4x%2B14y=44 Now go back to the first equation.


4x%2B14%282%29=44 Plug in y=2.


4x%2B28=44 Multiply.


4x=44-28 Subtract 28 from both sides.


4x=16 Combine like terms on the right side.


x=%2816%29%2F%284%29 Divide both sides by 4 to isolate x.


x=4 Reduce.


So our answer is x=4 and y=2.


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 2x%2B7y=22 (red) and -4x%2B9y=2 (green)