SOLUTION: 1. 3x=-5-x 2x+y=-5 2. 3x-5y=7 2x-y=-7 3. x-3y=1 3x-5y=-5

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: 1. 3x=-5-x 2x+y=-5 2. 3x-5y=7 2x-y=-7 3. x-3y=1 3x-5y=-5      Log On


   

Question 168738: 1.
3x=-5-x
2x+y=-5
2.
3x-5y=7
2x-y=-7
3.
x-3y=1
3x-5y=-5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1
Your first equation has two "x" variables. Is there a "y" term in the first equation?



# 2


Start with the given system of equations:
system%283x-5y=7%2C2x-y=-7%29


-5%282x-y%29=-5%28-7%29 Multiply the both sides of the second equation by -5.


-10x%2B5y=35 Distribute and multiply.


So we have the new system of equations:
system%283x-5y=7%2C-10x%2B5y=35%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:


%283x-5y%29%2B%28-10x%2B5y%29=%287%29%2B%2835%29


%283x%2B-10x%29%2B%28-5y%2B5y%29=7%2B35 Group like terms.


-7x%2B0y=42 Combine like terms. Notice how the y terms cancel out.


-7x=42 Simplify.


x=%2842%29%2F%28-7%29 Divide both sides by -7 to isolate x.


x=-6 Reduce.


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


3x-5y=7 Now go back to the first equation.


3%28-6%29-5y=7 Plug in x=-6.


-18-5y=7 Multiply.


-5y=7%2B18 Add 18 to both sides.


-5y=25 Combine like terms on the right side.


y=%2825%29%2F%28-5%29 Divide both sides by -5 to isolate y.


y=-5 Reduce.


So our answer is x=-6 and y=-5.


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-5y=7 (red) and 2x-y=-7 (green)




# 3



Start with the given system of equations:
system%28x-3y=1%2C3x-5y=-5%29


-3%28x-3y%29=-3%281%29 Multiply the both sides of the first equation by -3.


-3x%2B9y=-3 Distribute and multiply.


So we have the new system of equations:
system%28-3x%2B9y=-3%2C3x-5y=-5%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:


%28-3x%2B9y%29%2B%283x-5y%29=%28-3%29%2B%28-5%29


%28-3x%2B3x%29%2B%289y%2B-5y%29=-3%2B-5 Group like terms.


0x%2B4y=-8 Combine like terms. Notice how the x terms cancel out.


4y=-8 Simplify.


y=%28-8%29%2F%284%29 Divide both sides by 4 to isolate y.


y=-2 Reduce.


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


-3x%2B9y=-3 Now go back to the first equation.


-3x%2B9%28-2%29=-3 Plug in y=-2.


-3x-18=-3 Multiply.


-3x=-3%2B18 Add 18 to both sides.


-3x=15 Combine like terms on the right side.


x=%2815%29%2F%28-3%29 Divide both sides by -3 to isolate x.


x=-5 Reduce.


So our answer is x=-5 and y=-2.


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 x-3y=1 (red) and 3x-5y=-5 (green)