SOLUTION: solve: 3x-2y=12 2x+3y=-5 by the addition method solve: 2x-1y=-5 3x-5y=-4 by substitution show steps please.

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: solve: 3x-2y=12 2x+3y=-5 by the addition method solve: 2x-1y=-5 3x-5y=-4 by substitution show steps please.      Log On


   

Question 264538: solve:
3x-2y=12
2x+3y=-5
by the addition method

solve:
2x-1y=-5
3x-5y=-4
by substitution

show steps please.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started.




Start with the given system of equations:
system%283x-2y=12%2C2x%2B3y=-5%29


3%283x-2y%29=3%2812%29 Multiply the both sides of the first equation by 3.


9x-6y=36 Distribute and multiply.


2%282x%2B3y%29=2%28-5%29 Multiply the both sides of the second equation by 2.


4x%2B6y=-10 Distribute and multiply.


So we have the new system of equations:
system%289x-6y=36%2C4x%2B6y=-10%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%289x-6y%29%2B%284x%2B6y%29=%2836%29%2B%28-10%29


%289x%2B4x%29%2B%28-6y%2B6y%29=36%2B-10 Group like terms.


13x%2B0y=26 Combine like terms.


13x=26 Simplify.


x=%2826%29%2F%2813%29 Divide both sides by 13 to isolate x.


x=2 Reduce.


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


9x-6y=36 Now go back to the first equation.


9%282%29-6y=36 Plug in x=2.


18-6y=36 Multiply.


-6y=36-18 Subtract 18 from both sides.


-6y=18 Combine like terms on the right side.


y=%2818%29%2F%28-6%29 Divide both sides by -6 to isolate y.


y=-3 Reduce.


So the solutions are x=2 and y=-3.


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 3x-2y=12 (red) and 2x%2B3y=-5 (green)