SOLUTION: Help please! I tried this problem for hours and I couldn't figure it out. Also I need this problem done in in linear combination (elimination). -3x-10y=9 14x+18y=-22 Thanks!

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Help please! I tried this problem for hours and I couldn't figure it out. Also I need this problem done in in linear combination (elimination). -3x-10y=9 14x+18y=-22 Thanks!      Log On


   

Question 637179: Help please! I tried this problem for hours and I couldn't figure it out. Also I need this problem done in in linear combination (elimination).
-3x-10y=9
14x+18y=-22
Thanks!
Found 2 solutions by jim_thompson5910, MathTherapy:
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-10y=9%2C14x%2B18y=-22%29


9%28-3x-10y%29=9%289%29 Multiply the both sides of the first equation by 9.


-27x-90y=81 Distribute and multiply.


5%2814x%2B18y%29=5%28-22%29 Multiply the both sides of the second equation by 5.


70x%2B90y=-110 Distribute and multiply.


So we have the new system of equations:
system%28-27x-90y=81%2C70x%2B90y=-110%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:


%28-27x-90y%29%2B%2870x%2B90y%29=%2881%29%2B%28-110%29


%28-27x%2B70x%29%2B%28-90y%2B90y%29=81%2B-110 Group like terms.


43x%2B0y=-29 Combine like terms.


43x=-29 Simplify.


x=%28-29%29%2F%2843%29 Divide both sides by 43 to isolate x.


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


-27x-90y=81 Now go back to the first equation.


-27%28-29%2F43%29-90y=81 Plug in x=-29%2F43.


783%2F43-90y=81 Multiply.


43%28783%2Fcross%2843%29-90y%29=43%2881%29 Multiply both sides by the LCD 43 to clear any fractions.


783-3870y=3483 Distribute and multiply.


-3870y=3483-783 Subtract 783 from both sides.


-3870y=2700 Combine like terms on the right side.


y=%282700%29%2F%28-3870%29 Divide both sides by -3870 to isolate y.


y=-30%2F43 Reduce.


So the solutions are x=-29%2F43 and y=-30%2F43.


Which form the ordered pair .


This means that the system is consistent and independent.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Help please! I tried this problem for hours and I couldn't figure it out. Also I need this problem done in in linear combination (elimination).
-3x-10y=9
14x+18y=-22
Thanks!

- 3x - 10y = 9 ------ eq (i)
14x + 18y = - 22 ---- eq (ii)
- 27x - 90y = 81 ----- Multiplying eq (i) by 9 ------ eq (iii)
70x + 90y = - 110 ----- Multiplying eq (ii) by 5 ------ eq (iv)
43x = - 29 ------ Adding eqs (iv) & (iii)
x = highlight_green%28-+29%2F43%29

Now substitute -+29%2F43 for x into either eq (i) or (ii) and solve for y

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