Solve the System of Equations y+17=3(x+6)-14 y+15=x+6

$y + 17 = 3 (x + 6) - 14$ $y + 15 = x + 6$

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

Subtract $15$ from both sides of the equation.

$y = x + 6 - 15$

$y + 17 = 3 (x + 6) - 14$

Subtract $15$ from $6$ .

$y = x - 9$

$y + 17 = 3 (x + 6) - 14$

$y = x - 9$

$y + 17 = 3 (x + 6) - 14$

Replace all occurrences of $y$ with $x - 9$ in each equation.

Replace all occurrences of $y$ in $y + 17 = 3 (x + 6) - 14$ with $x - 9$ .

$(x - 9) + 17 = 3 (x + 6) - 14$

$y = x - 9$

Simplify $(x - 9) + 17 = 3 (x + 6) - 14$ .

Simplify the left side.

Add $- 9$ and $17$ .

$x + 8 = 3 (x + 6) - 14$

$y = x - 9$

$x + 8 = 3 (x + 6) - 14$

$y = x - 9$

Simplify the right side.

Simplify $3 (x + 6) - 14$ .

Simplify each term.

Apply the distributive property.

$x + 8 = 3 x + 3 \cdot 6 - 14$

$y = x - 9$

Multiply $3$ by $6$ .

$x + 8 = 3 x + 18 - 14$

$y = x - 9$

$x + 8 = 3 x + 18 - 14$

$y = x - 9$

Subtract $14$ from $18$ .

$x + 8 = 3 x + 4$

$y = x - 9$

$x + 8 = 3 x + 4$

$y = x - 9$

$x + 8 = 3 x + 4$

$y = x - 9$

$x + 8 = 3 x + 4$

$y = x - 9$

$x + 8 = 3 x + 4$

$y = x - 9$

Solve for $x$ in $x + 8 = 3 x + 4$ .

Move all terms containing $x$ to the left side of the equation.

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

$x + 8 - 3 x = 4$

$y = x - 9$

Subtract $3 x$ from $x$ .

$- 2 x + 8 = 4$

$y = x - 9$

$- 2 x + 8 = 4$

$y = x - 9$

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

Subtract $8$ from both sides of the equation.

$- 2 x = 4 - 8$

$y = x - 9$

Subtract $8$ from $4$ .

$- 2 x = - 4$

$y = x - 9$

$- 2 x = - 4$

$y = x - 9$

Divide each term in $- 2 x = - 4$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 4$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 4}{- 2}$

$y = x - 9$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 4}{- 2}$

$y = x - 9$

Divide $x$ by $1$ .

$x = \frac{- 4}{- 2}$

$y = x - 9$

$x = \frac{- 4}{- 2}$

$y = x - 9$

$x = \frac{- 4}{- 2}$

$y = x - 9$

Simplify the right side.

Divide $- 4$ by $- 2$ .

$x = 2$

$y = x - 9$

$x = 2$

$y = x - 9$

$x = 2$

$y = x - 9$

$x = 2$

$y = x - 9$

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

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

$y = (2) - 9$

$x = 2$

Simplify the right side.

Subtract $9$ from $2$ .

$y = - 7$

$x = 2$

$y = - 7$

$x = 2$

$y = - 7$

$x = 2$

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

$(2, - 7)$

The result can be shown in multiple forms.

Point Form:

$(2, - 7)$

Equation Form:

$x = 2, y = - 7$

Solve the System of Equations y+17=3(x+6)-14 y+15=x+6

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