SOLUTION: Solve each system using the specified method. Substitution 4x-3y=15 x-2y=0

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Solve each system using the specified method. Substitution 4x-3y=15 x-2y=0      Log On


   

Question 184141: Solve each system using the specified method. Substitution
4x-3y=15
x-2y=0
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%284x-3y=15%2Cx-2y=0%29


-4%28x-2y%29=-4%280%29 Multiply the both sides of the second equation by -4.


-4x%2B8y=0 Distribute and multiply.


So we have the new system of equations:
system%284x-3y=15%2C-4x%2B8y=0%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:


%284x-3y%29%2B%28-4x%2B8y%29=%2815%29%2B%280%29


%284x%2B-4x%29%2B%28-3y%2B8y%29=15%2B0 Group like terms.


0x%2B5y=15 Combine like terms.


5y=15 Simplify.


y=%2815%29%2F%285%29 Divide both sides by 5 to isolate y.


y=3 Reduce.


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


4x-3y=15 Now go back to the first equation.


4x-3%283%29=15 Plug in y=3.


4x-9=15 Multiply.


4x=15%2B9 Add 9 to both sides.


4x=24 Combine like terms on the right side.


x=%2824%29%2F%284%29 Divide both sides by 4 to isolate x.


x=6 Reduce.


So the solutions are x=6 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 4x-3y=15 (red) and x-2y=0 (green)