SOLUTION: 2x + 3y = 8 and 3x + 2y = 7

Question 197921This question is from textbook
: 2x + 3y = 8 and 3x + 2y = 7
This question is from textbook

Found 2 solutions by Ratman99, jim_thompson5910:
Answer by Ratman99(5) (Show Source): You can put this solution on YOUR website!
-987
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Ignore the other solution, I don't know what that is...

Start with the given system of equations:

Multiply the both sides of the first equation by 3.

Distribute and multiply.

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.

Subtract from both sides.

Combine like terms on the right side.

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.

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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