SOLUTION: solve: 3x-2y=12 2x+3y=-5 by the addition method solve: 2x-1y=-5 3x-5y=-4 by substitution show steps please.

Question 264538: solve:
3x-2y=12
2x+3y=-5
by the addition method

solve:
2x-1y=-5
3x-5y=-4
by substitution

show steps please.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first one to get you started.

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.

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

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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