SOLUTION: Solve the system & identify it as consistent, inconsistent or dependent. { 4x+y=8 4x+5y=-8 } a) (3,-4); consistent/dependent b) {(3,-4) l 4x+y=8}; consistent/dependent

Algebra ->  Matrices-and-determiminant -> SOLUTION: Solve the system & identify it as consistent, inconsistent or dependent. { 4x+y=8 4x+5y=-8 } a) (3,-4); consistent/dependent b) {(3,-4) l 4x+y=8}; consistent/dependent      Log On


   

Question 151524: Solve the system & identify it as consistent, inconsistent or dependent.
{ 4x+y=8
4x+5y=-8 }
a) (3,-4); consistent/dependent
b) {(3,-4) l 4x+y=8}; consistent/dependent
c) 0; inconsistent
d) (3,-4); consistent/independent
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%2By=8%2C4x%2B5y=-8%29


-1%284x%2B5y%29=-1%28-8%29 Multiply the both sides of the second equation by -1.


-4x-5y=8 Distribute and multiply.


So we have the new system of equations:
system%284x%2By=8%2C-4x-5y=8%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%2By%29%2B%28-4x-5y%29=%288%29%2B%288%29


%284x-4x%29%2B%28y-5y%29=8%2B8 Group like terms.


0x-4y=16 Combine like terms. Notice how the x terms cancel out.


-4y=16 Simplify.


y=%2816%29%2F%28-4%29 Divide both sides by -4 to isolate y.


y=-4 Reduce.


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


4x%2By=8 Now go back to the first equation.


4x-4=8 Plug in y=-4.


4x-4=8 Multiply.


4x=8%2B4 Add 4 to both sides.


4x=12 Combine like terms on the right side.


x=%2812%29%2F%284%29 Divide both sides by 4 to isolate x.


x=3 Reduce.


So our answer is x=3 and y=-4.


Which form the ordered pair .


This means that the system is consistent and independent.


So the answer is choice d) (3,-4); consistent/independent


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of 4x%2By=8 (red) and 4x%2B5y=-8 (green)