Solve the System of @WORD 3x+6y=6 , 4x+y=8

$3 x + 6 y = 6$ , $4 x + y = 8$

Step 1

Subtract $4 x$ from both sides of the equation.

$y = 8 - 4 x$

$3 x + 6 y = 6$

Step 2

Replace all occurrences of $y$ with $8 - 4 x$ in each equation.

Replace all occurrences of $y$ in $3 x + 6 y = 6$ with $8 - 4 x$ .

$3 x + 6 (8 - 4 x) = 6$

$y = 8 - 4 x$

Simplify the left side.

Simplify $3 x + 6 (8 - 4 x)$ .

Simplify each term.

Apply the distributive property.

$3 x + 6 \cdot 8 + 6 (- 4 x) = 6$

$y = 8 - 4 x$

Multiply $6$ by $8$ .

$3 x + 48 + 6 (- 4 x) = 6$

$y = 8 - 4 x$

Multiply $- 4$ by $6$ .

$3 x + 48 - 24 x = 6$

$y = 8 - 4 x$

$3 x + 48 - 24 x = 6$

$y = 8 - 4 x$

Subtract $24 x$ from $3 x$ .

$- 21 x + 48 = 6$

$y = 8 - 4 x$

$- 21 x + 48 = 6$

$y = 8 - 4 x$

$- 21 x + 48 = 6$

$y = 8 - 4 x$

$- 21 x + 48 = 6$

$y = 8 - 4 x$

Step 3

Solve for $x$ in $- 21 x + 48 = 6$ .

Move all terms not containing $x$ to the right side of the equation.

Subtract $48$ from both sides of the equation.

$- 21 x = 6 - 48$

$y = 8 - 4 x$

Subtract $48$ from $6$ .

$- 21 x = - 42$

$y = 8 - 4 x$

$- 21 x = - 42$

$y = 8 - 4 x$

Divide each term in $- 21 x = - 42$ by $- 21$ and simplify.

Divide each term in $- 21 x = - 42$ by $- 21$ .

$\frac{- 21 x}{- 21} = \frac{- 42}{- 21}$

$y = 8 - 4 x$

Simplify the left side.

Cancel the common factor of $- 21$ .

Cancel the common factor.

$\frac{- 21 x}{- 21} = \frac{- 42}{- 21}$

$y = 8 - 4 x$

Divide $x$ by $1$ .

$x = \frac{- 42}{- 21}$

$y = 8 - 4 x$

$x = \frac{- 42}{- 21}$

$y = 8 - 4 x$

$x = \frac{- 42}{- 21}$

$y = 8 - 4 x$

Simplify the right side.

Divide $- 42$ by $- 21$ .

$x = 2$

$y = 8 - 4 x$

$x = 2$

$y = 8 - 4 x$

$x = 2$

$y = 8 - 4 x$

$x = 2$

$y = 8 - 4 x$

Step 4

Replace all occurrences of $x$ with $2$ in each equation.

Replace all occurrences of $x$ in $y = 8 - 4 x$ with $2$ .

$y = 8 - 4 \cdot 2$

$x = 2$

Simplify the right side.

Simplify $8 - 4 \cdot 2$ .

Multiply $- 4$ by $2$ .

$y = 8 - 8$

$x = 2$

Subtract $8$ from $8$ .

$y = 0$

$x = 2$

$y = 0$

$x = 2$

$y = 0$

$x = 2$

$y = 0$

$x = 2$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(2, 0)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(2, 0)$

Equation Form:

$x = 2, y = 0$

Step 7

Solve the System of @WORD 3x+6y=6 , 4x+y=8

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