SOLUTION: please help me with this equations 3x-6y=24 4x+5y=-7

Algebra ->  Expressions-with-variables -> SOLUTION: please help me with this equations 3x-6y=24 4x+5y=-7      Log On


   

Question 151579: please help me with this equations
3x-6y=24
4x+5y=-7
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%283x-6y=24%2C4x%2B5y=-7%29


-4%283x-6y%29=-4%2824%29 Multiply the both sides of the first equation by -4.


-12x%2B24y=-96 Distribute and multiply.


3%284x%2B5y%29=3%28-7%29 Multiply the both sides of the second equation by 3.


12x%2B15y=-21 Distribute and multiply.


So we have the new system of equations:
system%28-12x%2B24y=-96%2C12x%2B15y=-21%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:


%28-12x%2B24y%29%2B%2812x%2B15y%29=%28-96%29%2B%28-21%29


%28-12x%2B12x%29%2B%2824y%2B15y%29=-96%2B-21 Group like terms.


0x%2B39y=-117 Combine like terms. Notice how the x terms cancel out.


39y=-117 Simplify.


y=%28-117%29%2F%2839%29 Divide both sides by 39 to isolate y.


y=-3 Reduce.


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


-12x%2B24y=-96 Now go back to the first equation.


-12x%2B24%28-3%29=-96 Plug in y=-3.


-12x-72=-96 Multiply.


-12x=-96%2B72 Add 72 to both sides.


-12x=-24 Combine like terms on the right side.


x=%28-24%29%2F%28-12%29 Divide both sides by -12 to isolate x.


x=2 Reduce.


So our answer is 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-6y=24 (red) and 4x%2B5y=-7 (green)