Solve the System of Equations 3x+y=-14 -2x-y=9

$3 x + y = - 14$ $- 2 x - y = 9$

Step 1

Subtract $3 x$ from both sides of the equation.

$y = - 14 - 3 x$

$- 2 x - y = 9$

Step 2

Replace all occurrences of $y$ with $- 14 - 3 x$ in each equation.

Replace all occurrences of $y$ in $- 2 x - y = 9$ with $- 14 - 3 x$ .

$- 2 x - (- 14 - 3 x) = 9$

$y = - 14 - 3 x$

Simplify the left side.

Simplify $- 2 x - (- 14 - 3 x)$ .

Simplify each term.

Apply the distributive property.

$- 2 x + 14 - (- 3 x) = 9$

$y = - 14 - 3 x$

Multiply $- 1$ by $- 14$ .

$- 2 x + 14 - (- 3 x) = 9$

$y = - 14 - 3 x$

Multiply $- 3$ by $- 1$ .

$- 2 x + 14 + 3 x = 9$

$y = - 14 - 3 x$

$- 2 x + 14 + 3 x = 9$

$y = - 14 - 3 x$

Add $- 2 x$ and $3 x$ .

$x + 14 = 9$

$y = - 14 - 3 x$

$x + 14 = 9$

$y = - 14 - 3 x$

$x + 14 = 9$

$y = - 14 - 3 x$

$x + 14 = 9$

$y = - 14 - 3 x$

Step 3

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

Subtract $14$ from both sides of the equation.

$x = 9 - 14$

$y = - 14 - 3 x$

Subtract $14$ from $9$ .

$x = - 5$

$y = - 14 - 3 x$

$x = - 5$

$y = - 14 - 3 x$

Step 4

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

Replace all occurrences of $x$ in $y = - 14 - 3 x$ with $- 5$ .

$y = - 14 - 3 \cdot - 5$

$x = - 5$

Simplify the right side.

Simplify $- 14 - 3 \cdot - 5$ .

Multiply $- 3$ by $- 5$ .

$y = - 14 + 15$

$x = - 5$

Add $- 14$ and $15$ .

$y = 1$

$x = - 5$

$y = 1$

$x = - 5$

$y = 1$

$x = - 5$

$y = 1$

$x = - 5$

Step 5

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

$(- 5, 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 5, 1)$

Equation Form:

$x = - 5, y = 1$

Step 7

Solve the System of Equations 3x+y=-14 -2x-y=9

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