Solve the System of Equations -x+4y=16 and 3x-y=7

$- x + 4 y = 16$ and $3 x - y = 7$

Step 1

Solve for $x$ in $- x + 4 y = 16$ .

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

$- x = 16 - 4 y$

$3 x - y = 7$

Divide each term in $- x = 16 - 4 y$ by $- 1$ and simplify.

Divide each term in $- x = 16 - 4 y$ by $- 1$ .

$\frac{- x}{- 1} = \frac{16}{- 1} + \frac{- 4 y}{- 1}$

$3 x - y = 7$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{16}{- 1} + \frac{- 4 y}{- 1}$

$3 x - y = 7$

Divide $x$ by $1$ .

$x = \frac{16}{- 1} + \frac{- 4 y}{- 1}$

$3 x - y = 7$

$x = \frac{16}{- 1} + \frac{- 4 y}{- 1}$

$3 x - y = 7$

Simplify the right side.

Simplify each term.

Divide $16$ by $- 1$ .

$x = - 16 + \frac{- 4 y}{- 1}$

$3 x - y = 7$

Move the negative one from the denominator of $\frac{- 4 y}{- 1}$ .

$x = - 16 - 1 \cdot (- 4 y)$

$3 x - y = 7$

Rewrite $- 1 \cdot (- 4 y)$ as $- (- 4 y)$ .

$x = - 16 - (- 4 y)$

$3 x - y = 7$

Multiply $- 4$ by $- 1$ .

$x = - 16 + 4 y$

$3 x - y = 7$

$x = - 16 + 4 y$

$3 x - y = 7$

$x = - 16 + 4 y$

$3 x - y = 7$

$x = - 16 + 4 y$

$3 x - y = 7$

$x = - 16 + 4 y$

$3 x - y = 7$

Step 2

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

Replace all occurrences of $x$ in $3 x - y = 7$ with $- 16 + 4 y$ .

$3 (- 16 + 4 y) - y = 7$

$x = - 16 + 4 y$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

$3 \cdot - 16 + 3 (4 y) - y = 7$

$x = - 16 + 4 y$

Multiply $3$ by $- 16$ .

$- 48 + 3 (4 y) - y = 7$

$x = - 16 + 4 y$

Multiply $4$ by $3$ .

$- 48 + 12 y - y = 7$

$x = - 16 + 4 y$

$- 48 + 12 y - y = 7$

$x = - 16 + 4 y$

Subtract $y$ from $12 y$ .

$- 48 + 11 y = 7$

$x = - 16 + 4 y$

$- 48 + 11 y = 7$

$x = - 16 + 4 y$

$- 48 + 11 y = 7$

$x = - 16 + 4 y$

$- 48 + 11 y = 7$

$x = - 16 + 4 y$

Step 3

Solve for $y$ in $- 48 + 11 y = 7$ .

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

Add $48$ to both sides of the equation.

$11 y = 7 + 48$

$x = - 16 + 4 y$

Add $7$ and $48$ .

$11 y = 55$

$x = - 16 + 4 y$

$11 y = 55$

$x = - 16 + 4 y$

Divide each term in $11 y = 55$ by $11$ and simplify.

Divide each term in $11 y = 55$ by $11$ .

$\frac{11 y}{11} = \frac{55}{11}$

$x = - 16 + 4 y$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 y}{11} = \frac{55}{11}$

$x = - 16 + 4 y$

Divide $y$ by $1$ .

$y = \frac{55}{11}$

$x = - 16 + 4 y$

$y = \frac{55}{11}$

$x = - 16 + 4 y$

$y = \frac{55}{11}$

$x = - 16 + 4 y$

Simplify the right side.

Divide $55$ by $11$ .

$y = 5$

$x = - 16 + 4 y$

$y = 5$

$x = - 16 + 4 y$

$y = 5$

$x = - 16 + 4 y$

$y = 5$

$x = - 16 + 4 y$

Step 4

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

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

$x = - 16 + 4 (5)$

$y = 5$

Simplify the right side.

Simplify $- 16 + 4 (5)$ .

Multiply $4$ by $5$ .

$x = - 16 + 20$

$y = 5$

Add $- 16$ and $20$ .

$x = 4$

$y = 5$

$x = 4$

$y = 5$

$x = 4$

$y = 5$

$x = 4$

$y = 5$

Step 5

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

$(4, 5)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, 5)$

Equation Form:

$x = 4, y = 5$

Step 7

Solve the System of Equations -x+4y=16 and 3x-y=7

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