SOLUTION: Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this. 8x + 10y = 92 24x + 11y = 162

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this. 8x + 10y = 92 24x + 11y = 162       Log On


   

Question 394381: Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
8x + 10y = 92
24x + 11y = 162
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%288x%2B10y=92%2C24x%2B11y=162%29


-3%288x%2B10y%29=-3%2892%29 Multiply the both sides of the first equation by -3.


-24x-30y=-276 Distribute and multiply.


So we have the new system of equations:
system%28-24x-30y=-276%2C24x%2B11y=162%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:


%28-24x-30y%29%2B%2824x%2B11y%29=%28-276%29%2B%28162%29


%28-24x%2B24x%29%2B%28-30y%2B11y%29=-276%2B162 Group like terms.


0x%2B-19y=-114 Combine like terms.


-19y=-114 Simplify.


y=%28-114%29%2F%28-19%29 Divide both sides by -19 to isolate y.


y=6 Reduce.


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-24x-30y=-276 Now go back to the first equation.


-24x-30%286%29=-276 Plug in y=6.


-24x-180=-276 Multiply.


-24x=-276%2B180 Add 180 to both sides.


-24x=-96 Combine like terms on the right side.


x=%28-96%29%2F%28-24%29 Divide both sides by -24 to isolate x.


x=4 Reduce.


So the solutions are x=4 and y=6.


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 8x%2B10y=92 (red) and 24x%2B11y=162 (green)


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim