SOLUTION: My question pertains to solving linear equations using subsitution method. Solve: 5x+2y = 0 x-3y = 0 Please show me detailed steps on doing a problem of this type - Thank y

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Question 113863: My question pertains to solving linear equations using subsitution method.
Solve:
5x+2y = 0
x-3y = 0
Please show me detailed steps on doing a problem of this type - Thank you kindly!
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Solving a linear system of equations by subsitution


Lets start with the given system of linear equations

5%2Ax%2B2%2Ay=0
1%2Ax-3%2Ay=0

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

2%2Ay=0-5%2AxSubtract 5%2Ax from both sides

y=%280-5%2Ax%29%2F2 Divide both sides by 2.


Which breaks down and reduces to



y=0-%285%2F2%29%2Ax Now we've fully isolated y

Since y equals 0-%285%2F2%29%2Ax we can substitute the expression 0-%285%2F2%29%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


1%2Ax%2B-3%2Ahighlight%28%280-%285%2F2%29%2Ax%29%29=0 Replace y with 0-%285%2F2%29%2Ax. Since this eliminates y, we can now solve for x.

1%2Ax-3%2A%280%29-3%28-5%2F2%29x=0 Distribute -3 to 0-%285%2F2%29%2Ax

1%2Ax%2B0%2B%2815%2F2%29%2Ax=0 Multiply



1%2Ax%2B0%2B%2815%2F2%29%2Ax=0 Reduce any fractions

1%2Ax%2B%2815%2F2%29%2Ax=0%2B0Add 0 to both sides


1%2Ax%2B%2815%2F2%29%2Ax=0 Combine the terms on the right side



%282%2F2%29%2Ax%2B%2815%2F2%29x=0 Make 1 into a fraction with a denominator of 2

%2817%2F2%29%2Ax=0 Now combine the terms on the left side.


cross%28%282%2F17%29%2817%2F2%29%29x=%280%2F1%29%282%2F17%29 Multiply both sides by 2%2F17. This will cancel out 17%2F2 and isolate x

So when we multiply 0%2F1 and 2%2F17 (and simplify) we get



x=0 <---------------------------------One answer

Now that we know that x=0, lets substitute that in for x to solve for y

1%280%29-3%2Ay=0 Plug in x=0 into the 2nd equation

0-3%2Ay=0 Multiply

-3%2Ay=0%2B0Add 0 to both sides

-3%2Ay=0 Combine the terms on the right side

cross%28%281%2F-3%29%28-3%29%29%2Ay=%280%2F1%29%281%2F-3%29 Multiply both sides by 1%2F-3. This will cancel out -3 on the left side.

y=0%2F-3 Multiply the terms on the right side


y=%2B0 Reduce


So this is the other answer


y=%2B0<---------------------------------Other answer


So our solution is

x=0 and y=%2B0

which can also look like

(0,%2B0)

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

5%2Ax%2B2%2Ay=0
1%2Ax-3%2Ay=0

we get


%0D%0A++drawing%28+500%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A++++graph%28+500%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%280-5%2Ax%29%2F2%2C+%280-1%2Ax%29%2F-3+%29%2C%0D%0A++++blue%28++circle%28+0%2C+-0%2C+0.133333333333333+%29+%29+%0D%0A++%29%0D%0A++graph of 5%2Ax%2B2%2Ay=0 (red) and 1%2Ax-3%2Ay=0 (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 (0,%2B0). This verifies our answer.


-----------------------------------------------------------------------------------------------
Check:

Plug in (0,%2B0) into the system of equations


Let x=0 and y=%2B0. Now plug those values into the equation 5%2Ax%2B2%2Ay=0

5%2A%280%29%2B2%2A%28%2B0%29=0 Plug in x=0 and y=%2B0


0%2B0=0 Multiply


0=0 Add


0=0 Reduce. Since this equation is true the solution works.


So the solution (0,%2B0) satisfies 5%2Ax%2B2%2Ay=0



Let x=0 and y=%2B0. Now plug those values into the equation 1%2Ax-3%2Ay=0

1%2A%280%29-3%2A%28%2B0%29=0 Plug in x=0 and y=%2B0


0%2B0=0 Multiply


0=0 Add


0=0 Reduce. Since this equation is true the solution works.


So the solution (0,%2B0) satisfies 1%2Ax-3%2Ay=0


Since the solution (0,%2B0) satisfies the system of equations


5%2Ax%2B2%2Ay=0
1%2Ax-3%2Ay=0


this verifies our answer.