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

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) (Show Source): You can put this solution on YOUR website!
Start with the given system of equations:

Multiply the both sides of the first equation by the LCD 5.

Distribute and multiply.

Now multiply the both sides of the first equation by -2.

Distribute and multiply.

So we have the new system of equations:

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

Group like terms.

Combine like terms. Notice how the x terms cancel out.

Simplify.

Divide both sides by to isolate .

Reduce.

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

Now go back to the first equation.

Plug in .

Multiply.

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So our answer is and .

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 (red) and (green)

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