Solve the System of @WORD 2x+4y=4 , 4x+y=8

$2 x + 4 y = 4$ , $4 x + y = 8$

Step 1

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

$y = 8 - 4 x$

$2 x + 4 y = 4$

Step 2

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

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

$2 x + 4 (8 - 4 x) = 4$

$y = 8 - 4 x$

Simplify the left side.

Simplify $2 x + 4 (8 - 4 x)$ .

Simplify each term.

Apply the distributive property.

$2 x + 4 \cdot 8 + 4 (- 4 x) = 4$

$y = 8 - 4 x$

Multiply $4$ by $8$ .

$2 x + 32 + 4 (- 4 x) = 4$

$y = 8 - 4 x$

Multiply $- 4$ by $4$ .

$2 x + 32 - 16 x = 4$

$y = 8 - 4 x$

$2 x + 32 - 16 x = 4$

$y = 8 - 4 x$

Subtract $16 x$ from $2 x$ .

$- 14 x + 32 = 4$

$y = 8 - 4 x$

$- 14 x + 32 = 4$

$y = 8 - 4 x$

$- 14 x + 32 = 4$

$y = 8 - 4 x$

$- 14 x + 32 = 4$

$y = 8 - 4 x$

Step 3

Solve for $x$ in $- 14 x + 32 = 4$ .

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

Subtract $32$ from both sides of the equation.

$- 14 x = 4 - 32$

$y = 8 - 4 x$

Subtract $32$ from $4$ .

$- 14 x = - 28$

$y = 8 - 4 x$

$- 14 x = - 28$

$y = 8 - 4 x$

Divide each term in $- 14 x = - 28$ by $- 14$ and simplify.

Divide each term in $- 14 x = - 28$ by $- 14$ .

$\frac{- 14 x}{- 14} = \frac{- 28}{- 14}$

$y = 8 - 4 x$

Simplify the left side.

Cancel the common factor of $- 14$ .

Cancel the common factor.

$\frac{- 14 x}{- 14} = \frac{- 28}{- 14}$

$y = 8 - 4 x$

Divide $x$ by $1$ .

$x = \frac{- 28}{- 14}$

$y = 8 - 4 x$

$x = \frac{- 28}{- 14}$

$y = 8 - 4 x$

$x = \frac{- 28}{- 14}$

$y = 8 - 4 x$

Simplify the right side.

Divide $- 28$ by $- 14$ .

$x = 2$

$y = 8 - 4 x$

$x = 2$

$y = 8 - 4 x$

$x = 2$

$y = 8 - 4 x$

$x = 2$

$y = 8 - 4 x$

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 2x+4y=4 , 4x+y=8

Related Questions

Support LCMGCF.com by disabling your adblocker.