Solve the System of Equations 4x+y=16 2x+3y=-2

$4 x + y = 16$ $2 x + 3 y = - 2$

Step 1

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

$y = 16 - 4 x$

$2 x + 3 y = - 2$

Step 2

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

Replace all occurrences of $y$ in $2 x + 3 y = - 2$ with $16 - 4 x$ .

$2 x + 3 (16 - 4 x) = - 2$

$y = 16 - 4 x$

Simplify the left side.

Simplify $2 x + 3 (16 - 4 x)$ .

Simplify each term.

Apply the distributive property.

$2 x + 3 \cdot 16 + 3 (- 4 x) = - 2$

$y = 16 - 4 x$

Multiply $3$ by $16$ .

$2 x + 48 + 3 (- 4 x) = - 2$

$y = 16 - 4 x$

Multiply $- 4$ by $3$ .

$2 x + 48 - 12 x = - 2$

$y = 16 - 4 x$

$2 x + 48 - 12 x = - 2$

$y = 16 - 4 x$

Subtract $12 x$ from $2 x$ .

$- 10 x + 48 = - 2$

$y = 16 - 4 x$

$- 10 x + 48 = - 2$

$y = 16 - 4 x$

$- 10 x + 48 = - 2$

$y = 16 - 4 x$

$- 10 x + 48 = - 2$

$y = 16 - 4 x$

Step 3

Solve for $x$ in $- 10 x + 48 = - 2$ .

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

Subtract $48$ from both sides of the equation.

$- 10 x = - 2 - 48$

$y = 16 - 4 x$

Subtract $48$ from $- 2$ .

$- 10 x = - 50$

$y = 16 - 4 x$

$- 10 x = - 50$

$y = 16 - 4 x$

Divide each term in $- 10 x = - 50$ by $- 10$ and simplify.

Divide each term in $- 10 x = - 50$ by $- 10$ .

$\frac{- 10 x}{- 10} = \frac{- 50}{- 10}$

$y = 16 - 4 x$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 x}{- 10} = \frac{- 50}{- 10}$

$y = 16 - 4 x$

Divide $x$ by $1$ .

$x = \frac{- 50}{- 10}$

$y = 16 - 4 x$

$x = \frac{- 50}{- 10}$

$y = 16 - 4 x$

$x = \frac{- 50}{- 10}$

$y = 16 - 4 x$

Simplify the right side.

Divide $- 50$ by $- 10$ .

$x = 5$

$y = 16 - 4 x$

$x = 5$

$y = 16 - 4 x$

$x = 5$

$y = 16 - 4 x$

$x = 5$

$y = 16 - 4 x$

Step 4

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

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

$y = 16 - 4 \cdot 5$

$x = 5$

Simplify the right side.

Simplify $16 - 4 \cdot 5$ .

Multiply $- 4$ by $5$ .

$y = 16 - 20$

$x = 5$

Subtract $20$ from $16$ .

$y = - 4$

$x = 5$

$y = - 4$

$x = 5$

$y = - 4$

$x = 5$

$y = - 4$

$x = 5$

Step 5

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

$(5, - 4)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(5, - 4)$

Equation Form:

$x = 5, y = - 4$

Step 7

Solve the System of Equations 4x+y=16 2x+3y=-2

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