SOLUTION: Solve by addition method. Determine whether the equation is independent, dependent, or inconsistent. 28. -3x + 2y = 8 3x + 2y = 8

Algebra ->  Linear-equations -> SOLUTION: Solve by addition method. Determine whether the equation is independent, dependent, or inconsistent. 28. -3x + 2y = 8 3x + 2y = 8      Log On


   

Question 134465: Solve by addition method. Determine whether the equation is independent, dependent, or inconsistent.
28. -3x + 2y = 8
3x + 2y = 8
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%28-3x%2B2y=8%2C3x%2B2y=8%29


Add the equations together. In order to add 2 equations, group like terms and combine them

%28-3x%2B3x%29%2B%282y%2B2y%29=8%2B8

Combine like terms and simplify



cross%28-3x%2B3x%29%2B4y=16 Notice how the x terms cancel out




4y=16 Simplify




y=16%2F4 Divide both sides by 4 to isolate y




y=4 Reduce



Now plug this answer into the top equation -3x%2B2y=8 to solve for x

-3x%2B2y=8 Start with the first equation



-3x%2B2%284%29=8 Plug in y=4




-3x%2B8=8 Multiply



-3x=8-8Subtract 8 from both sides


-3x=0 Combine like terms on the right side


x=%280%29%2F%28-3%29 Divide both sides by -3 to isolate x



x=0 Divide




So our answer is
x=0 and y=4



which also looks like




Now let's graph the two equations (if you need help with graphing, check out this solver)


From the graph, we can see that the two equations intersect at . This visually verifies our answer.




graph of -3x%2B2y=8 (red) and 3x%2B2y=8 (green) and the intersection of the lines (blue circle).