SOLUTION: I have gotten thru 4 of the 8 questions on my worksheet and am stuck with this one. the direction say to "solve each system by elimination" 12x - 7y = -10 -4x + 3y = 10 I

Algebra ->  Expressions-with-variables -> SOLUTION: I have gotten thru 4 of the 8 questions on my worksheet and am stuck with this one. the direction say to "solve each system by elimination" 12x - 7y = -10 -4x + 3y = 10 I       Log On


   

Question 198012: I have gotten thru 4 of the 8 questions on my worksheet and am stuck with this one. the direction say to "solve each system by elimination"
12x - 7y = -10
-4x + 3y = 10
I can't seem to get either side to cancel out.
Found 2 solutions by jim_thompson5910, josmiceli:
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%2812x-7y=-10%2C-4x%2B3y=10%29


3%28-4x%2B3y%29=3%2810%29 Multiply the both sides of the second equation by 3.


-12x%2B9y=30 Distribute and multiply.


So we have the new system of equations:
system%2812x-7y=-10%2C-12x%2B9y=30%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:


%2812x-7y%29%2B%28-12x%2B9y%29=%28-10%29%2B%2830%29


%2812x%2B-12x%29%2B%28-7y%2B9y%29=-10%2B30 Group like terms.


0x%2B2y=20 Combine like terms.


2y=20 Simplify.


y=%2820%29%2F%282%29 Divide both sides by 2 to isolate y.


y=10 Reduce.


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


12x-7y=-10 Now go back to the first equation.


12x-7%2810%29=-10 Plug in y=10.


12x-70=-10 Multiply.


12x=-10%2B70 Add 70 to both sides.


12x=60 Combine like terms on the right side.


x=%2860%29%2F%2812%29 Divide both sides by 12 to isolate x.


x=5 Reduce.


So the solutions are x=5 and y=10.


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 12x-7y=-10 (red) and -4x%2B3y=10 (green)

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
12x+-+7y+=+-10
-4x+%2B+3y+=+10
Multiply both sides of the 2nd equation by 3
and add the equations
12x+-+7y+=+-10
-12x+%2B+9y+=+30
--------------------
2y+=+20
y+=+10
Plug this result back in to 2nd equation
-4x+%2B+3y+=+10
-4x+%2B+3%2A10+=+10
-4x+=+10+-+30
-4x+=+-20
x+=+5
The solution is x+=+5,y+=+10
check:
12%2A5+-+7%2A10+=+-10
60+-+70+=+-10
-10+=+-10
and
-4%2A5+%2B+3%2A10+=+10
-20+%2B+30+=+10
10+=+10
OK