SOLUTION: 2x-4y=40 8x-3y=82 Is there no solution for this problem? I can't come up with anything that works. I need to show work but can't solve it. Thanks

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: 2x-4y=40 8x-3y=82 Is there no solution for this problem? I can't come up with anything that works. I need to show work but can't solve it. Thanks       Log On


   

Question 637131: 2x-4y=40
8x-3y=82
Is there no solution for this problem? I can't come up with anything that works. I need to show work but can't solve it. Thanks
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-4y=40%2C8x-3y=82%29


3%282x-4y%29=3%2840%29 Multiply the both sides of the first equation by 3.


6x-12y=120 Distribute and multiply.


-4%288x-3y%29=-4%2882%29 Multiply the both sides of the second equation by -4.


-32x%2B12y=-328 Distribute and multiply.


So we have the new system of equations:
system%286x-12y=120%2C-32x%2B12y=-328%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-12y%29%2B%28-32x%2B12y%29=%28120%29%2B%28-328%29


%286x%2B-32x%29%2B%28-12y%2B12y%29=120%2B-328 Group like terms.


-26x%2B0y=-208 Combine like terms.


-26x=-208 Simplify.


x=%28-208%29%2F%28-26%29 Divide both sides by -26 to isolate x.


x=8 Reduce.


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


6x-12y=120 Now go back to the first equation.


6%288%29-12y=120 Plug in x=8.


48-12y=120 Multiply.


-12y=120-48 Subtract 48 from both sides.


-12y=72 Combine like terms on the right side.


y=%2872%29%2F%28-12%29 Divide both sides by -12 to isolate y.


y=-6 Reduce.


So the solutions are x=8 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 2x-4y=40 (red) and 8x-3y=82 (green)