SOLUTION: 2x+3y=4 x+4y=6

Question 201434: 2x+3y=4
x+4y=6
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 second 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.

Simplify.

Divide both sides by to isolate .

Reduce.

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Now go back to the first equation.

Plug in .

Multiply.

Multiply both sides by the LCD to clear any fractions.

Distribute and multiply.

Subtract 24 from both sides.

Combine like terms.

Divide both sides by to isolate .

Reduce.

So the solutions are and .

Which form the ordered pair

.

This means that the system is consistent and independent.

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