SOLUTION: Solve each system by the addition method: 3/7x+5/9y=27 1/9x+2/7y=7

Question 147009: Solve each system by the addition method:
3/7x+5/9y=27
1/9x+2/7y=7
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the first equation.

Multiply both sides by the LCD to clear any fractions.

Distribute and multiply.

Now move onto the next equation.

Multiply both sides by the LCD to clear any fractions.

Distribute and multiply.

Start with the given system of equations:

Multiply the both sides of the first equation by -7.

Distribute and multiply.

Multiply the both sides of the second equation by 27.

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.

Remove any zero terms.

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.

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