SOLUTION: Solve the system by the addition method. Determine whether the equations are independent, dependent, or inconsistent. 3x - 2y = -7 x – 5y = 2

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve the system by the addition method. Determine whether the equations are independent, dependent, or inconsistent. 3x - 2y = -7 x – 5y = 2       Log On


   

Question 207149: Solve the system by the addition method. Determine whether the equations are independent, dependent, or inconsistent.
3x - 2y = -7
x – 5y = 2
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-2y=-7%2Cx-5y=2%29


-3%28x-5y%29=-3%282%29 Multiply the both sides of the second equation by -3.


-3x%2B15y=-6 Distribute and multiply.


So we have the new system of equations:
system%283x-2y=-7%2C-3x%2B15y=-6%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-2y%29%2B%28-3x%2B15y%29=%28-7%29%2B%28-6%29


%283x%2B-3x%29%2B%28-2y%2B15y%29=-7%2B-6 Group like terms.


0x%2B13y=-13 Combine like terms.


13y=-13 Simplify.


y=%28-13%29%2F%2813%29 Divide both sides by 13 to isolate y.


y=-1 Reduce.


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3x-2y=-7 Now go back to the first equation.


3x-2%28-1%29=-7 Plug in y=-1.


3x%2B2=-7 Multiply.


3x=-7-2 Subtract 2 from both sides.


3x=-9 Combine like terms on the right side.


x=%28-9%29%2F%283%29 Divide both sides by 3 to isolate x.


x=-3 Reduce.


So the solutions are x=-3 and y=-1.


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