SOLUTION: Solve 3x+2y=-6 -2x+5y=23 and classify the system

Question 173315This question is from textbook Saxon Algebra 2
: Solve
3x+2y=-6
-2x+5y=23
and classify the system This question is from textbook Saxon Algebra 2

Found 2 solutions by jim_thompson5910, Mathtut:
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 2.

Distribute and multiply.

Multiply the both sides of the second equation by 3.

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 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)

Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
3x+2y=-6....eq 1
-2x+5y=23....eq 2
lets use the process of elimination which means we need to manipulate eq 1 and 2 such that one of the variables is eliminated. There are various numbers we could multiply by the equations to reach this objective. Lets multiply eq 1 by 5 and eq 2 by -2 so that the y terms will be eliminated
:
15x+10y=-30...revised eq 1
4x-10y=-46....revised eq 2
:
now observing the equations we can see that when the equations are added to one another that the y terms are eliminated 10y-10y=0. We are left with
15x+4x=-30-46
:
19x=-76
:

:
now we take x's found value and plug it back into any equation to find y's value. I choose eq 1
:
3(-4)+2y=-6
:
-12+2y=-6
:
2y=6
:

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