SOLUTION: Solve the following system of equations, and check: 2x+3y=-4 5x+2y=1

Question 198423: Solve the following system of equations, and check:
2x+3y=-4
5x+2y=1

Found 2 solutions by jim_thompson5910, m.keenan:
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.

Simplify.

Divide both sides by to isolate .

Reduce.

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

Now go back to the first equation.

Plug in .

Multiply.

Add to 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)
Answer by m.keenan(1) (Show Source): You can put this solution on YOUR website!
Solve the following system of equations, and check:
2x+3y=-4 (1)
5x+2y=1 (2) label equations
= 2x+3y=-4 (1) *2
5x+2y=1 (2) *3
=4x+6y=-8 (3)
15x+6y=3 (4) label new equations
Therefore: 4x+6y-(15x+6y)=-8-3
=4x+6y-15x-6y=-11
= -11x= =11
= x=1
Now we can sub x=1 back into any labelled equation.
2(1) +3y=-4
=3y=-6
y=-2
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