SOLUTION: Please solve each system -5x + 2y = 9 -3x + 8y = -15

Question 374762: Please solve each system
-5x + 2y = 9
-3x + 8y = -15
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 -4.

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)

If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim
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