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

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)   (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:

Any system of equations:

has solution

or

(x=6.66666666666667, y=-0.333333333333333}

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

Start with the given system of equations:

Start with the first equation.

Subtract from both sides.

Divide both sides by to isolate .

Rearrange the terms and simplify.

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

Move onto the second equation.

Now plug in .

Distribute.

Combine like terms on the left side.

Add to both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

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

Since we know that , we can use this to find .

Go back to the first equation.

Plug in .

Multiply both sides by the LCD to clear any fractions.

Distribute and multiply.

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So the solutions are and .

which form the ordered pair

This means that the system is consistent and independent.

Answer by MathTherapy(10552)   (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

Substitute this value for y in equation (ii):

, or , or

(,)

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