SOLUTION: Iam not in understanding of the substitution method can someone please help? 4x+6y=16 6x +y =3

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Question 483077: Iam not in understanding of the substitution method can someone please help?

4x+6y=16
6x +y =3
Found 2 solutions by MathLover1, lwsshak3:
Answer by MathLover1(20850) 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

4%2Ax%2B6%2Ay=16
6%2Ax%2B1%2Ay=3

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

6%2Ay=16-4%2AxSubtract 4%2Ax from both sides

y=%2816-4%2Ax%29%2F6 Divide both sides by 6.


Which breaks down and reduces to



y=8%2F3-%282%2F3%29%2Ax Now we've fully isolated y

Since y equals 8%2F3-%282%2F3%29%2Ax we can substitute the expression 8%2F3-%282%2F3%29%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


6%2Ax%2B1%2Ahighlight%28%288%2F3-%282%2F3%29%2Ax%29%29=3 Replace y with 8%2F3-%282%2F3%29%2Ax. Since this eliminates y, we can now solve for x.

6%2Ax%2B1%2A%288%2F3%29%2B1%28-2%2F3%29x=3 Distribute 1 to 8%2F3-%282%2F3%29%2Ax

6%2Ax%2B8%2F3-%282%2F3%29%2Ax=3 Multiply



6%2Ax%2B8%2F3-%282%2F3%29%2Ax=3 Reduce any fractions

6%2Ax-%282%2F3%29%2Ax=3-8%2F3 Subtract 8%2F3 from both sides


6%2Ax-%282%2F3%29%2Ax=9%2F3-8%2F3 Make 3 into a fraction with a denominator of 3


6%2Ax-%282%2F3%29%2Ax=1%2F3 Combine the terms on the right side



%2818%2F3%29%2Ax-%282%2F3%29x=1%2F3 Make 6 into a fraction with a denominator of 3

%2816%2F3%29%2Ax=1%2F3 Now combine the terms on the left side.


cross%28%283%2F16%29%2816%2F3%29%29x=%281%2F3%29%283%2F16%29 Multiply both sides by 3%2F16. This will cancel out 16%2F3 and isolate x

So when we multiply 1%2F3 and 3%2F16 (and simplify) we get



x=1%2F16 <---------------------------------One answer

Now that we know that x=1%2F16, lets substitute that in for x to solve for y

6%281%2F16%29%2B1%2Ay=3 Plug in x=1%2F16 into the 2nd equation

3%2F8%2B1%2Ay=3 Multiply

1%2Ay=3-3%2F8Subtract 3%2F8 from both sides

1%2Ay=24%2F8-3%2F8 Make 3 into a fraction with a denominator of 8



1%2Ay=21%2F8 Combine the terms on the right side

cross%28%281%2F1%29%281%29%29%2Ay=%2821%2F8%29%281%2F1%29 Multiply both sides by 1%2F1. This will cancel out 1 on the left side.

y=21%2F8 Multiply the terms on the right side


y=21%2F8 Reduce


So this is the other answer


y=21%2F8<---------------------------------Other answer


So our solution is

x=1%2F16 and y=21%2F8

which can also look like

(1%2F16,21%2F8)

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

4%2Ax%2B6%2Ay=16
6%2Ax%2B1%2Ay=3

we get


graph of 4%2Ax%2B6%2Ay=16 (red) and 6%2Ax%2B1%2Ay=3 (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 (1%2F16,21%2F8). This verifies our answer.


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Check:

Plug in (1%2F16,21%2F8) into the system of equations


Let x=1%2F16 and y=21%2F8. Now plug those values into the equation 4%2Ax%2B6%2Ay=16

4%2A%281%2F16%29%2B6%2A%2821%2F8%29=16 Plug in x=1%2F16 and y=21%2F8


4%2F16%2B126%2F8=16 Multiply


256%2F16=16 Add


16=16 Reduce. Since this equation is true the solution works.


So the solution (1%2F16,21%2F8) satisfies 4%2Ax%2B6%2Ay=16



Let x=1%2F16 and y=21%2F8. Now plug those values into the equation 6%2Ax%2B1%2Ay=3

6%2A%281%2F16%29%2B1%2A%2821%2F8%29=3 Plug in x=1%2F16 and y=21%2F8


6%2F16%2B21%2F8=3 Multiply


48%2F16=3 Add


3=3 Reduce. Since this equation is true the solution works.


So the solution (1%2F16,21%2F8) satisfies 6%2Ax%2B1%2Ay=3


Since the solution (1%2F16,21%2F8) satisfies the system of equations


4%2Ax%2B6%2Ay=16
6%2Ax%2B1%2Ay=3


this verifies our answer.

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Iam not in understanding of the substitution method can someone please help?
4x+6y=16
6x +y =3
**
Solve for y in the second equation
y=3-6x
sub 3-6x for y in first equation
4x+6(3-6x)=16
4x+18-36x=16
-32x=-2
x=2/32=1/16