SOLUTION: System of Linear Equations: Solve the system using the addition method. 2x+3y=-16 5x-10y=30

Algebra ->  Trigonometry-basics -> SOLUTION: System of Linear Equations: Solve the system using the addition method. 2x+3y=-16 5x-10y=30      Log On


   

Question 152165: System of Linear Equations:
Solve the system using the addition method.
2x+3y=-16
5x-10y=30
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%282x%2B3y=-16%2C5x-10y=30%29


5%282x%2B3y%29=5%28-16%29 Multiply the both sides of the first equation by 5.


10x%2B15y=-80 Distribute and multiply.


-2%285x-10y%29=-2%2830%29 Multiply the both sides of the second equation by -2.


-10x%2B20y=-60 Distribute and multiply.


So we have the new system of equations:
system%2810x%2B15y=-80%2C-10x%2B20y=-60%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:


%2810x%2B15y%29%2B%28-10x%2B20y%29=%28-80%29%2B%28-60%29


%2810x%2B-10x%29%2B%2815y%2B20y%29=-80%2B-60 Group like terms.


0x%2B35y=-140 Combine like terms. Notice how the x terms cancel out.


35y=-140 Simplify.


y=%28-140%29%2F%2835%29 Divide both sides by 35 to isolate y.


y=-4 Reduce.


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


10x%2B15y=-80 Now go back to the first equation.


10x%2B15%28-4%29=-80 Plug in y=-4.


10x-60=-80 Multiply.


10x=-80%2B60 Add 60 to both sides.


10x=-20 Combine like terms on the right side.


x=%28-20%29%2F%2810%29 Divide both sides by 10 to isolate x.


x=-2 Reduce.


So our answer is x=-2 and y=-4.


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 2x%2B3y=-16 (red) and 5x-10y=30 (green)