Solve the System of Equations 2y=-x+9 3x-6y=-15

$2 y = - x + 9$ $3 x - 6 y = - 15$

Divide each term in $2 y = - x + 9$ by $2$ and simplify.

Divide each term in $2 y = - x + 9$ by $2$ .

$\frac{2 y}{2} = \frac{- x}{2} + \frac{9}{2}$

$3 x - 6 y = - 15$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{- x}{2} + \frac{9}{2}$

$3 x - 6 y = - 15$

Divide $y$ by $1$ .

$y = \frac{- x}{2} + \frac{9}{2}$

$3 x - 6 y = - 15$

$y = \frac{- x}{2} + \frac{9}{2}$

$3 x - 6 y = - 15$

$y = \frac{- x}{2} + \frac{9}{2}$

$3 x - 6 y = - 15$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{x}{2} + \frac{9}{2}$

$3 x - 6 y = - 15$

$y = - \frac{x}{2} + \frac{9}{2}$

$3 x - 6 y = - 15$

$y = - \frac{x}{2} + \frac{9}{2}$

$3 x - 6 y = - 15$

Replace all occurrences of $y$ with $- \frac{x}{2} + \frac{9}{2}$ in each equation.

Replace all occurrences of $y$ in $3 x - 6 y = - 15$ with $- \frac{x}{2} + \frac{9}{2}$ .

$3 x - 6 (- \frac{x}{2} + \frac{9}{2}) = - 15$

$y = - \frac{x}{2} + \frac{9}{2}$

Simplify the left side.

Simplify $3 x - 6 (- \frac{x}{2} + \frac{9}{2})$ .

Simplify each term.

Apply the distributive property.

$3 x - 6 (- \frac{x}{2}) - 6 (\frac{9}{2}) = - 15$

$y = - \frac{x}{2} + \frac{9}{2}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{x}{2}$ into the numerator.

$3 x - 6 \frac{- x}{2} - 6 (\frac{9}{2}) = - 15$

$y = - \frac{x}{2} + \frac{9}{2}$

Factor $2$ out of $- 6$ .

$3 x + 2 (- 3) (\frac{- x}{2}) - 6 (\frac{9}{2}) = - 15$

$y = - \frac{x}{2} + \frac{9}{2}$

Cancel the common factor.

$3 x + 2 \cdot (- 3 \frac{- x}{2}) - 6 (\frac{9}{2}) = - 15$

$y = - \frac{x}{2} + \frac{9}{2}$

Rewrite the expression.

$3 x - 3 (- x) - 6 (\frac{9}{2}) = - 15$

$y = - \frac{x}{2} + \frac{9}{2}$

$3 x - 3 (- x) - 6 (\frac{9}{2}) = - 15$

$y = - \frac{x}{2} + \frac{9}{2}$

Multiply $- 1$ by $- 3$ .

$3 x + 3 x - 6 (\frac{9}{2}) = - 15$

$y = - \frac{x}{2} + \frac{9}{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $- 6$ .

$3 x + 3 x + 2 (- 3) (\frac{9}{2}) = - 15$

$y = - \frac{x}{2} + \frac{9}{2}$

Cancel the common factor.

$3 x + 3 x + 2 \cdot (- 3 (\frac{9}{2})) = - 15$

$y = - \frac{x}{2} + \frac{9}{2}$

Rewrite the expression.

$3 x + 3 x - 3 \cdot 9 = - 15$

$y = - \frac{x}{2} + \frac{9}{2}$

$3 x + 3 x - 3 \cdot 9 = - 15$

$y = - \frac{x}{2} + \frac{9}{2}$

Multiply $- 3$ by $9$ .

$3 x + 3 x - 27 = - 15$

$y = - \frac{x}{2} + \frac{9}{2}$

$3 x + 3 x - 27 = - 15$

$y = - \frac{x}{2} + \frac{9}{2}$

Add $3 x$ and $3 x$ .

$6 x - 27 = - 15$

$y = - \frac{x}{2} + \frac{9}{2}$

$6 x - 27 = - 15$

$y = - \frac{x}{2} + \frac{9}{2}$

$6 x - 27 = - 15$

$y = - \frac{x}{2} + \frac{9}{2}$

$6 x - 27 = - 15$

$y = - \frac{x}{2} + \frac{9}{2}$

Solve for $x$ in $6 x - 27 = - 15$ .

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

Add $27$ to both sides of the equation.

$6 x = - 15 + 27$

$y = - \frac{x}{2} + \frac{9}{2}$

Add $- 15$ and $27$ .

$6 x = 12$

$y = - \frac{x}{2} + \frac{9}{2}$

$6 x = 12$

$y = - \frac{x}{2} + \frac{9}{2}$

Divide each term in $6 x = 12$ by $6$ and simplify.

Divide each term in $6 x = 12$ by $6$ .

$\frac{6 x}{6} = \frac{12}{6}$

$y = - \frac{x}{2} + \frac{9}{2}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{12}{6}$

$y = - \frac{x}{2} + \frac{9}{2}$

Divide $x$ by $1$ .

$x = \frac{12}{6}$

$y = - \frac{x}{2} + \frac{9}{2}$

$x = \frac{12}{6}$

$y = - \frac{x}{2} + \frac{9}{2}$

$x = \frac{12}{6}$

$y = - \frac{x}{2} + \frac{9}{2}$

Simplify the right side.

Divide $12$ by $6$ .

$x = 2$

$y = - \frac{x}{2} + \frac{9}{2}$

$x = 2$

$y = - \frac{x}{2} + \frac{9}{2}$

$x = 2$

$y = - \frac{x}{2} + \frac{9}{2}$

$x = 2$

$y = - \frac{x}{2} + \frac{9}{2}$

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

Replace all occurrences of $x$ in $y = - \frac{x}{2} + \frac{9}{2}$ with $2$ .

$y = - \frac{2}{2} + \frac{9}{2}$

$x = 2$

Simplify the right side.

Simplify $- \frac{2}{2} + \frac{9}{2}$ .

Combine the numerators over the common denominator.

$y = \frac{- 2 + 9}{2}$

$x = 2$

Add $- 2$ and $9$ .

$y = \frac{7}{2}$

$x = 2$

$y = \frac{7}{2}$

$x = 2$

$y = \frac{7}{2}$

$x = 2$

$y = \frac{7}{2}$

$x = 2$

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

$(2, \frac{7}{2})$

The result can be shown in multiple forms.

Point Form:

$(2, \frac{7}{2})$

Equation Form:

$x = 2, y = \frac{7}{2}$

Related Questions