SOLUTION: Solve the system by substitution. x + 5y = 0 –2x – 4y = 6 A) (–5, -1) B) (5, 1) C) (–5, 1) D) (5, -1) I need help with the above question please.

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Solve the system by substitution. x + 5y = 0 –2x – 4y = 6 A) (–5, -1) B) (5, 1) C) (–5, 1) D) (5, -1) I need help with the above question please.       Log On


   

Question 92527: Solve the system by substitution.
x + 5y = 0
–2x – 4y = 6
A) (–5, -1) B) (5, 1) C) (–5, 1) D) (5, -1)
I need help with the above question please.



Answer by jim_thompson5910(35256) 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

1%2Ax%2B5%2Ay=0
-2%2Ax-4%2Ay=6

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

5%2Ay=0-1%2AxSubtract 1%2Ax from both sides

y=%280-1%2Ax%29%2F5 Divide both sides by 5.


Which breaks down and reduces to



y=0-%281%2F5%29%2Ax Now we've fully isolated y

Since y equals 0-%281%2F5%29%2Ax we can substitute the expression 0-%281%2F5%29%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


-2%2Ax%2B-4%2Ahighlight%28%280-%281%2F5%29%2Ax%29%29=6 Replace y with 0-%281%2F5%29%2Ax. Since this eliminates y, we can now solve for x.

-2%2Ax-4%2A%280%29-4%28-1%2F5%29x=6 Distribute -4 to 0-%281%2F5%29%2Ax

-2%2Ax%2B0%2B%284%2F5%29%2Ax=6 Multiply



-2%2Ax%2B0%2B%284%2F5%29%2Ax=6 Reduce any fractions

-2%2Ax%2B%284%2F5%29%2Ax=6%2B0Add 0 to both sides


-2%2Ax%2B%284%2F5%29%2Ax=6 Combine the terms on the right side



%28-10%2F5%29%2Ax%2B%284%2F5%29x=6 Make -2 into a fraction with a denominator of 5

%28-6%2F5%29%2Ax=6 Now combine the terms on the left side.


cross%28%285%2F-6%29%28-6%2F5%29%29x=%286%2F1%29%285%2F-6%29 Multiply both sides by 5%2F-6. This will cancel out -6%2F5 and isolate x

So when we multiply 6%2F1 and 5%2F-6 (and simplify) we get



x=-5 <---------------------------------One answer

Now that we know that x=-5, lets substitute that in for x to solve for y

-2%28-5%29-4%2Ay=6 Plug in x=-5 into the 2nd equation

10-4%2Ay=6 Multiply

-4%2Ay=6-10Subtract 10 from both sides

-4%2Ay=-4 Combine the terms on the right side

cross%28%281%2F-4%29%28-4%29%29%2Ay=%28-4%2F1%29%281%2F-4%29 Multiply both sides by 1%2F-4. This will cancel out -4 on the left side.

y=-4%2F-4 Multiply the terms on the right side


y=1 Reduce


So this is the other answer


y=1<---------------------------------Other answer


So our solution is

x=-5 and y=1

which can also look like

(-5,1)

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

1%2Ax%2B5%2Ay=0
-2%2Ax-4%2Ay=6

we get


graph of 1%2Ax%2B5%2Ay=0 (red) and -2%2Ax-4%2Ay=6 (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 (-5,1). This verifies our answer.


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

Plug in (-5,1) into the system of equations


Let x=-5 and y=1. Now plug those values into the equation 1%2Ax%2B5%2Ay=0

1%2A%28-5%29%2B5%2A%281%29=0 Plug in x=-5 and y=1


-5%2B5=0 Multiply


0=0 Add


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


So the solution (-5,1) satisfies 1%2Ax%2B5%2Ay=0



Let x=-5 and y=1. Now plug those values into the equation -2%2Ax-4%2Ay=6

-2%2A%28-5%29-4%2A%281%29=6 Plug in x=-5 and y=1


10-4=6 Multiply


6=6 Add


6=6 Reduce. Since this equation is true the solution works.


So the solution (-5,1) satisfies -2%2Ax-4%2Ay=6


Since the solution (-5,1) satisfies the system of equations


1%2Ax%2B5%2Ay=0
-2%2Ax-4%2Ay=6


this verifies our answer.





So the answer is C)