SOLUTION: I can not determine the answer to: 13x-3y=-50 { 12x+5y=16 in either the substitution method or the elimination method..

Question 183398: I can not determine the answer to:
13x-3y=-50
{
12x+5y=16
in either the substitution method or the elimination method..
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'm going to use elimination to solve this system:

Start with the first equation

Multiply both sides by 5

Distribute and multiply.

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

Move onto the second equation

Multiply both sides 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 y terms cancel out.

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 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 solver91311(24713) (Show Source): You can put this solution on YOUR website!

Multiply (1) by 5 and (2) by 3:

Add the two equations:

Solve for x, then substitute the value found for x into either (1) or (2) to solve for y.

John

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