SOLUTION: I am trying to solve the following system of linear equation. x/4 - y/11 = -9/44 x/6 - y/13 = -1/26 Now i am familiar with the methods of solving these types of problems,

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: I am trying to solve the following system of linear equation. x/4 - y/11 = -9/44 x/6 - y/13 = -1/26 Now i am familiar with the methods of solving these types of problems,      Log On


   

Question 148123: I am trying to solve the following system of linear equation.
x/4 - y/11 = -9/44
x/6 - y/13 = -1/26
Now i am familiar with the methods of solving these types of problems, such as addition method and substitution method, but when it comes to fractions, I'm lost.
When you solve, would it be possible to explain each step.
Thanks for all your help.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F4-y%2F11=-9%2F44 Start with the first equation.


44%28x%2Fcross%284%29-y%2Fcross%2811%29%29=44%28-9%2Fcross%2844%29%29 Multiply both sides by the LCD 44 to clear any fractions.


11x-4y=-9 Distribute and multiply.

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x%2F6-y%2F13=-1%2F26 Move onto the second equation.


78%28x%2Fcross%286%29-y%2Fcross%2813%29%29=78%28-1%2Fcross%2826%29%29 Multiply both sides by the LCD 78 to clear any fractions.


13x-6y=-3 Distribute and multiply.



So now we have the system system%2811x-4y=-9%2C13x-6y=-3%29

Let's solve this system by use of elimination.


6%2811x-4y%29=6%28-9%29 Multiply the both sides of the first equation by 6.


66x-24y=-54 Distribute and multiply.


-4%2813x-6y%29=-4%28-3%29 Multiply the both sides of the second equation by -4.


-52x%2B24y=12 Distribute and multiply.


So we have the new system of equations:
system%2866x-24y=-54%2C-52x%2B24y=12%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:


%2866x-24y%29%2B%28-52x%2B24y%29=%28-54%29%2B%2812%29


%2866x%2B-52x%29%2B%28-24y%2B24y%29=-54%2B12 Group like terms.


14x%2B0y=-42 Combine like terms. Notice how the y terms cancel out.


14x=-42 Simplify.


x=%28-42%29%2F%2814%29 Divide both sides by 14 to isolate x.


x=-3 Reduce.


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66x-24y=-54 Now go back to the first equation.


66%28-3%29-24y=-54 Plug in x=-3.


-198-24y=-54 Multiply.


-24y=-54%2B198 Add 198 to both sides.


-24y=144 Combine like terms on the right side.


y=%28144%29%2F%28-24%29 Divide both sides by -24 to isolate y.


y=-6 Reduce.


So our answer is x=-3 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 11x-4y=-9 (red) and 13x-6y=-3 (green)