SOLUTION: Solve the System 3/4x + 2/5y = 13 1/3x - -3/10y = 1 can I get help on solving to the answer? here is what I have so far... 3/4x + 2/5y = 13 -3/4x -3/4x .......

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve the System 3/4x + 2/5y = 13 1/3x - -3/10y = 1 can I get help on solving to the answer? here is what I have so far... 3/4x + 2/5y = 13 -3/4x -3/4x .......      Log On


   

Question 781993: Solve the System
3/4x + 2/5y = 13
1/3x - -3/10y = 1
can I get help on solving to the answer? here is what I have so far...
3/4x + 2/5y = 13
-3/4x -3/4x
..........
2/5y = 13 - 3/4x.
That's all I have. It s the fractions that are confusing me. Can I get rid of them of do I have to actually add/sub them like normal?
Help would be appreciated!!!! thank you!
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Solving a linear system of equations by subsitution


%283%2F4%29%2Ax%2B%282%2F5%29%2Ay=13 Start with the first equation


20%28%283%2F4%29%2Ax%2B%282%2F5%29%2Ay%29=%2820%29%2A%2813%29 Multiply both sides by the LCD 20



15%2Ax%2B8%2Ay=260Distribute and simplify


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%281%2F3%29%2Ax%2B%283%2F10%29%2Ay=1 Start with the second equation


30%28%281%2F3%29%2Ax%2B%283%2F10%29%2Ay%29=%2830%29%2A%281%29 Multiply both sides by the LCD 30



10%2Ax%2B9%2Ay=30 Distribute and simplify


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Lets start with the given system of linear equations

15%2Ax%2B8%2Ay=260
10%2Ax%2B9%2Ay=30

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to choose y.

Solve for y for the first equation

8%2Ay=260-15%2AxSubtract 15%2Ax from both sides

y=%28260-15%2Ax%29%2F8 Divide both sides by 8.


Which breaks down and reduces to



y=65%2F2-%2815%2F8%29%2Ax Now we've fully isolated y

Since y equals 65%2F2-%2815%2F8%29%2Ax we can substitute the expression 65%2F2-%2815%2F8%29%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


10%2Ax%2B9%2Ahighlight%28%2865%2F2-%2815%2F8%29%2Ax%29%29=30 Replace y with 65%2F2-%2815%2F8%29%2Ax. Since this eliminates y, we can now solve for x.

10%2Ax%2B9%2A%2865%2F2%29%2B9%28-15%2F8%29x=30 Distribute 9 to 65%2F2-%2815%2F8%29%2Ax

10%2Ax%2B585%2F2-%28135%2F8%29%2Ax=30 Multiply



10%2Ax%2B585%2F2-%28135%2F8%29%2Ax=30 Reduce any fractions

10%2Ax-%28135%2F8%29%2Ax=30-585%2F2 Subtract 585%2F2 from both sides


10%2Ax-%28135%2F8%29%2Ax=60%2F2-585%2F2 Make 30 into a fraction with a denominator of 2


10%2Ax-%28135%2F8%29%2Ax=-525%2F2 Combine the terms on the right side



%2880%2F8%29%2Ax-%28135%2F8%29x=-525%2F2 Make 10 into a fraction with a denominator of 8

%28-55%2F8%29%2Ax=-525%2F2 Now combine the terms on the left side.


cross%28%288%2F-55%29%28-55%2F8%29%29x=%28-525%2F2%29%288%2F-55%29 Multiply both sides by 8%2F-55. This will cancel out -55%2F8 and isolate x

So when we multiply -525%2F2 and 8%2F-55 (and simplify) we get



x=420%2F11 <---------------------------------One answer

Now that we know that x=420%2F11, lets substitute that in for x to solve for y

10%28420%2F11%29%2B9%2Ay=30 Plug in x=420%2F11 into the 2nd equation

4200%2F11%2B9%2Ay=30 Multiply

9%2Ay=30-4200%2F11Subtract 4200%2F11 from both sides

9%2Ay=330%2F11-4200%2F11 Make 30 into a fraction with a denominator of 11



9%2Ay=-3870%2F11 Combine the terms on the right side

cross%28%281%2F9%29%289%29%29%2Ay=%28-3870%2F11%29%281%2F9%29 Multiply both sides by 1%2F9. This will cancel out 9 on the left side.

y=-3870%2F99 Multiply the terms on the right side


y=-430%2F11 Reduce


So this is the other answer


y=-430%2F11<---------------------------------Other answer


So our solution is

x=420%2F11 and y=-430%2F11

which can also look like

(420%2F11,-430%2F11)

Notice if we graph the equations (if you need help with graphing, check out this solver)

15%2Ax%2B8%2Ay=260
10%2Ax%2B9%2Ay=30

we get


graph of 15%2Ax%2B8%2Ay=260 (red) and 10%2Ax%2B9%2Ay=30 (green) (hint: you may have to solve for y to graph these) intersecting at the blue circle.


and we can see that the two equations intersect at (420%2F11,-430%2F11). This verifies our answer.


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Check:

Plug in (420%2F11,-430%2F11) into the system of equations


Let x=420%2F11 and y=-430%2F11. Now plug those values into the equation 15%2Ax%2B8%2Ay=260

15%2A%28420%2F11%29%2B8%2A%28-430%2F11%29=260 Plug in x=420%2F11 and y=-430%2F11


6300%2F11-3440%2F11=260 Multiply


2860%2F11=260 Add


260=260 Reduce. Since this equation is true the solution works.


So the solution (420%2F11,-430%2F11) satisfies 15%2Ax%2B8%2Ay=260



Let x=420%2F11 and y=-430%2F11. Now plug those values into the equation 10%2Ax%2B9%2Ay=30

10%2A%28420%2F11%29%2B9%2A%28-430%2F11%29=30 Plug in x=420%2F11 and y=-430%2F11


4200%2F11-3870%2F11=30 Multiply


330%2F11=30 Add


30=30 Reduce. Since this equation is true the solution works.


So the solution (420%2F11,-430%2F11) satisfies 10%2Ax%2B9%2Ay=30


Since the solution (420%2F11,-430%2F11) satisfies the system of equations


15%2Ax%2B8%2Ay=260
10%2Ax%2B9%2Ay=30


this verifies our answer.