SOLUTION: solve each system by any method 1 x-3y=1 3x-5y=-5 2 2x-3y=5 4x-6y=3

Question 168732: solve each system by any method
1 x-3y=1
3x-5y=-5
2 2x-3y=5
4x-6y=3
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 1

Substitution:

Start with the first equation

Add 3y to both sides.

Move onto the second equation

Plug in

Distribute.

Combine like terms on the left side.

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

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

Go back to the first isolated equation

Plug in

Multiply

Add

================================

So the solutions are and which form the ordered pair (-5, -2)

# 2

Elimination:

Start with the given system of equations:

Multiply the both sides of the first 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. Notice how the x terms cancel out.

Simplify.

Since is never true, this means that there are no solutions. So the system is inconsistent.

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