Solve the System of Equations 3x+4y=14 x+2y=-2

$3 x + 4 y = 14$ $x + 2 y = - 2$

Subtract $2 y$ from both sides of the equation.

$x = - 2 - 2 y$

$3 x + 4 y = 14$

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

Replace all occurrences of $x$ in $3 x + 4 y = 14$ with $- 2 - 2 y$ .

$3 (- 2 - 2 y) + 4 y = 14$

$x = - 2 - 2 y$

Simplify the left side.

Simplify $3 (- 2 - 2 y) + 4 y$ .

Simplify each term.

Apply the distributive property.

$3 \cdot - 2 + 3 (- 2 y) + 4 y = 14$

$x = - 2 - 2 y$

Multiply $3$ by $- 2$ .

$- 6 + 3 (- 2 y) + 4 y = 14$

$x = - 2 - 2 y$

Multiply $- 2$ by $3$ .

$- 6 - 6 y + 4 y = 14$

$x = - 2 - 2 y$

$- 6 - 6 y + 4 y = 14$

$x = - 2 - 2 y$

Add $- 6 y$ and $4 y$ .

$- 6 - 2 y = 14$

$x = - 2 - 2 y$

$- 6 - 2 y = 14$

$x = - 2 - 2 y$

$- 6 - 2 y = 14$

$x = - 2 - 2 y$

$- 6 - 2 y = 14$

$x = - 2 - 2 y$

Solve for $y$ in $- 6 - 2 y = 14$ .

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

Add $6$ to both sides of the equation.

$- 2 y = 14 + 6$

$x = - 2 - 2 y$

Add $14$ and $6$ .

$- 2 y = 20$

$x = - 2 - 2 y$

$- 2 y = 20$

$x = - 2 - 2 y$

Divide each term in $- 2 y = 20$ by $- 2$ and simplify.

Divide each term in $- 2 y = 20$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{20}{- 2}$

$x = - 2 - 2 y$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{20}{- 2}$

$x = - 2 - 2 y$

Divide $y$ by $1$ .

$y = \frac{20}{- 2}$

$x = - 2 - 2 y$

$y = \frac{20}{- 2}$

$x = - 2 - 2 y$

$y = \frac{20}{- 2}$

$x = - 2 - 2 y$

Simplify the right side.

Divide $20$ by $- 2$ .

$y = - 10$

$x = - 2 - 2 y$

$y = - 10$

$x = - 2 - 2 y$

$y = - 10$

$x = - 2 - 2 y$

$y = - 10$

$x = - 2 - 2 y$

Replace all occurrences of $y$ with $- 10$ in each equation.

Replace all occurrences of $y$ in $x = - 2 - 2 y$ with $- 10$ .

$x = - 2 - 2 \cdot - 10$

$y = - 10$

Simplify the right side.

Simplify $- 2 - 2 \cdot - 10$ .

Multiply $- 2$ by $- 10$ .

$x = - 2 + 20$

$y = - 10$

Add $- 2$ and $20$ .

$x = 18$

$y = - 10$

$x = 18$

$y = - 10$

$x = 18$

$y = - 10$

$x = 18$

$y = - 10$

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

$(18, - 10)$

The result can be shown in multiple forms.

Point Form:

$(18, - 10)$

Equation Form:

$x = 18, y = - 10$

Solve the System of Equations 3x+4y=14 x+2y=-2

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