SOLUTION: Solve This Equation by Using the Substitution Method. x+2y=6 x-4y=8

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Question 202661: Solve This Equation by Using the Substitution Method.
x+2y=6
x-4y=8
Found 3 solutions by dyakobovitch, jim_thompson5910, MathTherapy:
Answer by dyakobovitch(40) About Me  (Show Source):
You can put this solution on YOUR website!
Below is a solution for linear substitution:
Solved by pluggable solver: Linear System solver (using determinant)
Solve:
+system%28+%0D%0A++++1%5Cx+%2B+2%5Cy+=+6%2C%0D%0A++++1%5Cx+%2B+-4%5Cy+=+8+%29%0D%0A++

Any system of equations:


has solution

or



(x=6.66666666666667, y=-0.333333333333333}

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:


system%28x%2B2y=6%2Cx-4y=8%29


x%2B2y=6 Start with the first equation.


2y=6-x Subtract x from both sides.


y=%286-x%29%2F%282%29 Divide both sides by 2 to isolate y.


y=-%281%2F2%29x%2B3 Rearrange the terms and simplify.


-------------------------------------------


x-4y=8 Move onto the second equation.


x-4%28-%281%2F2%29x%2B3%29=8 Now plug in y=-%281%2F2%29x%2B3.


x%2B2x-12=8 Distribute.


3x-12=8 Combine like terms on the left side.


3x=8%2B12 Add 12 to both sides.


3x=20 Combine like terms on the right side.


x=%2820%29%2F%283%29 Divide both sides by 3 to isolate x.


-------------------------------------------


Since we know that x=20%2F3, we can use this to find y.


x%2B2y=6 Go back to the first equation.


20%2F3%2B2y=6 Plug in x=20%2F3.


3%2820%2Fcross%283%29%2B2y%29=3%286%29 Multiply both sides by the LCD 3 to clear any fractions.


20%2B6y=18 Distribute and multiply.


6y=18-20 Subtract 20 from both sides.


6y=-2 Combine like terms on the right side.


y=%28-2%29%2F%286%29 Divide both sides by 6 to isolate y.


y=-1%2F3 Reduce.


So the solutions are x=20%2F3 and y=-1%2F3.


which form the ordered pair


This means that the system is consistent and independent.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Solving for x in equation (i), we get x = 6 – 2y

Substitute this value for x in equation (ii). This gives us:

6 – 2y – 4y = 8
- 6y = 2
y++=++-1%2F3
Substitute this value for y in equation (ii): x+-+4%28-1%2F3%29+=+8

x+%2B+4%2F3+=+8, or x+=+8+-+4%2F3, or x+=+20%2F3

(highlight%2820%2F3%29,highlight%28-1%2F3%29)