SOLUTION: Solve the system of Equations 2/5x + 3/5y = 16/5 4x + 2y = 40 I know that some way you have to eliminate the fractions in the first equations. Where I am stuck at is how to

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Solve the system of Equations 2/5x + 3/5y = 16/5 4x + 2y = 40 I know that some way you have to eliminate the fractions in the first equations. Where I am stuck at is how to       Log On


   

Question 146532: Solve the system of Equations
2/5x + 3/5y = 16/5
4x + 2y = 40
I know that some way you have to eliminate the fractions in the first equations. Where I am stuck at is how to eliminate the fractions and what type of method to use to solve it.
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%28%282%2F5%29x+%2B+%283%2F5%29y+=+16%2F5%2C4x+%2B+2y+=+40%29


5%28%282%2Fcross%285%29%29x+%2B+%283%2Fcross%285%29%29y+%29=5%28+16%2Fcross%285%29%29 Multiply the both sides of the first equation by the LCD 5.


2x%2B3y=16 Distribute and multiply.


-2%282x%2B3y%29=-2%2816%29 Now multiply the both sides of the first equation by -2.


-4x-6y=-32 Distribute and multiply.


So we have the new system of equations:
system%28-4x-6y=-32%2C4x%2B2y=40%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:


%28-4x-6y%29%2B%284x%2B2y%29=%28-32%29%2B%2840%29


%28-4x%2B4x%29%2B%28-6y%2B2y%29=-32%2B40 Group like terms.


0x%2B-4y=8 Combine like terms. Notice how the x terms cancel out.


-4y=8 Simplify.


y=%288%29%2F%28-4%29 Divide both sides by -4 to isolate y.


y=-2 Reduce.


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-4x-6y=-32 Now go back to the first equation.


-4x-6%28-2%29=-32 Plug in y=-2.


-4x%2B12=-32 Multiply.


-4x=-32-12 Subtract 12 from both sides.


-4x=-44 Combine like terms on the right side.


x=%28-44%29%2F%28-4%29 Divide both sides by -4 to isolate x.


x=11 Reduce.


So our answer is x=11 and y=-2.


Which form the ordered pair .


This means that the two equations are consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of %282%2F5%29x+%2B+%283%2F5%29y+=+16%2F5 (red) and 4x+%2B+2y+=+40 (green)