Solve by Substitution x=16-4y and 3x+4y=8

$x = 16 - 4 y$ and $3 x + 4 y = 8$

Reorder $16$ and $- 4 y$ .

$x = - 4 y + 16$

$3 x + 4 y = 8$

Replace all occurrences of $x$ with $- 4 y + 16$ in each equation.

Replace all occurrences of $x$ in $3 x + 4 y = 8$ with $- 4 y + 16$ .

$3 (- 4 y + 16) + 4 y = 8$

$x = - 4 y + 16$

Simplify the left side.

Simplify $3 (- 4 y + 16) + 4 y$ .

Simplify each term.

Apply the distributive property.

$3 (- 4 y) + 3 \cdot 16 + 4 y = 8$

$x = - 4 y + 16$

Multiply $- 4$ by $3$ .

$- 12 y + 3 \cdot 16 + 4 y = 8$

$x = - 4 y + 16$

Multiply $3$ by $16$ .

$- 12 y + 48 + 4 y = 8$

$x = - 4 y + 16$

$- 12 y + 48 + 4 y = 8$

$x = - 4 y + 16$

Add $- 12 y$ and $4 y$ .

$- 8 y + 48 = 8$

$x = - 4 y + 16$

$- 8 y + 48 = 8$

$x = - 4 y + 16$

$- 8 y + 48 = 8$

$x = - 4 y + 16$

$- 8 y + 48 = 8$

$x = - 4 y + 16$

Solve for $y$ in $- 8 y + 48 = 8$ .

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

Subtract $48$ from both sides of the equation.

$- 8 y = 8 - 48$

$x = - 4 y + 16$

Subtract $48$ from $8$ .

$- 8 y = - 40$

$x = - 4 y + 16$

$- 8 y = - 40$

$x = - 4 y + 16$

Divide each term in $- 8 y = - 40$ by $- 8$ and simplify.

Divide each term in $- 8 y = - 40$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{- 40}{- 8}$

$x = - 4 y + 16$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{- 40}{- 8}$

$x = - 4 y + 16$

Divide $y$ by $1$ .

$y = \frac{- 40}{- 8}$

$x = - 4 y + 16$

$y = \frac{- 40}{- 8}$

$x = - 4 y + 16$

$y = \frac{- 40}{- 8}$

$x = - 4 y + 16$

Simplify the right side.

Divide $- 40$ by $- 8$ .

$y = 5$

$x = - 4 y + 16$

$y = 5$

$x = - 4 y + 16$

$y = 5$

$x = - 4 y + 16$

$y = 5$

$x = - 4 y + 16$

Replace all occurrences of $y$ with $5$ in each equation.

Replace all occurrences of $y$ in $x = - 4 y + 16$ with $5$ .

$x = - 4 \cdot 5 + 16$

$y = 5$

Simplify the right side.

Simplify $- 4 \cdot 5 + 16$ .

Multiply $- 4$ by $5$ .

$x = - 20 + 16$

$y = 5$

Add $- 20$ and $16$ .

$x = - 4$

$y = 5$

$x = - 4$

$y = 5$

$x = - 4$

$y = 5$

$x = - 4$

$y = 5$

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

$(- 4, 5)$

The result can be shown in multiple forms.

Point Form:

$(- 4, 5)$

Equation Form:

$x = - 4, y = 5$

Solve by Substitution x=16-4y and 3x+4y=8

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