Solve the System of Equations 6x+5y=2 3x+1/2y=-7

$6 x + 5 y = 2$ $3 x + \frac{1}{2} y = - 7$

Solve for $x$ in $6 x + 5 y = 2$ .

Subtract $5 y$ from both sides of the equation.

$6 x = 2 - 5 y$

$3 x + \frac{1}{2} y = - 7$

Divide each term in $6 x = 2 - 5 y$ by $6$ and simplify.

Divide each term in $6 x = 2 - 5 y$ by $6$ .

$\frac{6 x}{6} = \frac{2}{6} + \frac{- 5 y}{6}$

$3 x + \frac{1}{2} y = - 7$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{2}{6} + \frac{- 5 y}{6}$

$3 x + \frac{1}{2} y = - 7$

Divide $x$ by $1$ .

$x = \frac{2}{6} + \frac{- 5 y}{6}$

$3 x + \frac{1}{2} y = - 7$

$x = \frac{2}{6} + \frac{- 5 y}{6}$

$3 x + \frac{1}{2} y = - 7$

$x = \frac{2}{6} + \frac{- 5 y}{6}$

$3 x + \frac{1}{2} y = - 7$

Simplify the right side.

Simplify each term.

Cancel the common factor of $2$ and $6$ .

Factor $2$ out of $2$ .

$x = \frac{2 (1)}{6} + \frac{- 5 y}{6}$

$3 x + \frac{1}{2} y = - 7$

Cancel the common factors.

Factor $2$ out of $6$ .

$x = \frac{2 \cdot 1}{2 \cdot 3} + \frac{- 5 y}{6}$

$3 x + \frac{1}{2} y = - 7$

Cancel the common factor.

$x = \frac{2 \cdot 1}{2 \cdot 3} + \frac{- 5 y}{6}$

$3 x + \frac{1}{2} y = - 7$

Rewrite the expression.

$x = \frac{1}{3} + \frac{- 5 y}{6}$

$3 x + \frac{1}{2} y = - 7$

$x = \frac{1}{3} + \frac{- 5 y}{6}$

$3 x + \frac{1}{2} y = - 7$

$x = \frac{1}{3} + \frac{- 5 y}{6}$

$3 x + \frac{1}{2} y = - 7$

Move the negative in front of the fraction.

$x = \frac{1}{3} - \frac{5 y}{6}$

$3 x + \frac{1}{2} y = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

$3 x + \frac{1}{2} y = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

$3 x + \frac{1}{2} y = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

$3 x + \frac{1}{2} y = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

$3 x + \frac{1}{2} y = - 7$

Replace all occurrences of $x$ with $\frac{1}{3} - \frac{5 y}{6}$ in each equation.

Replace all occurrences of $x$ in $3 x + \frac{1}{2} y = - 7$ with $\frac{1}{3} - \frac{5 y}{6}$ .

$3 (\frac{1}{3} - \frac{5 y}{6}) + \frac{1}{2} y = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

Simplify the left side.

Simplify $3 (\frac{1}{3} - \frac{5 y}{6}) + \frac{1}{2} y$ .

Simplify each term.

Apply the distributive property.

$3 (\frac{1}{3}) + 3 (- \frac{5 y}{6}) + \frac{1}{2} y = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

Cancel the common factor of $3$ .

Cancel the common factor.

$3 (\frac{1}{3}) + 3 (- \frac{5 y}{6}) + \frac{1}{2} y = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

Rewrite the expression.

$1 + 3 (- \frac{5 y}{6}) + \frac{1}{2} y = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

$1 + 3 (- \frac{5 y}{6}) + \frac{1}{2} y = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{5 y}{6}$ into the numerator.

$1 + 3 (\frac{- 5 y}{6}) + \frac{1}{2} y = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

Factor $3$ out of $6$ .

$1 + 3 (\frac{- 5 y}{3 (2)}) + \frac{1}{2} y = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

Cancel the common factor.

$1 + 3 (\frac{- 5 y}{3 \cdot 2}) + \frac{1}{2} y = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

Rewrite the expression.

$1 + \frac{- 5 y}{2} + \frac{1}{2} y = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

$1 + \frac{- 5 y}{2} + \frac{1}{2} y = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

Move the negative in front of the fraction.

$1 - \frac{5 y}{2} + \frac{1}{2} y = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

Combine $\frac{1}{2}$ and $y$ .

$1 - \frac{5 y}{2} + \frac{y}{2} = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

$1 - \frac{5 y}{2} + \frac{y}{2} = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

Simplify terms.

Combine the numerators over the common denominator.

$1 + \frac{- 5 y + y}{2} = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

Add $- 5 y$ and $y$ .

$1 + \frac{- 4 y}{2} = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

Cancel the common factor of $- 4$ and $2$ .

Factor $2$ out of $- 4 y$ .

$1 + \frac{2 (- 2 y)}{2} = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

Cancel the common factors.

Factor $2$ out of $2$ .

$1 + \frac{2 (- 2 y)}{2 (1)} = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

Cancel the common factor.

$1 + \frac{2 (- 2 y)}{2 \cdot 1} = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

Rewrite the expression.

$1 + \frac{- 2 y}{1} = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

Divide $- 2 y$ by $1$ .

$1 - 2 y = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

$1 - 2 y = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

$1 - 2 y = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

$1 - 2 y = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

$1 - 2 y = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

$1 - 2 y = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

$1 - 2 y = - 7$

$x = \frac{1}{3} - \frac{5 y}{6}$

Solve for $y$ in $1 - 2 y = - 7$ .

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

Subtract $1$ from both sides of the equation.

$- 2 y = - 7 - 1$

$x = \frac{1}{3} - \frac{5 y}{6}$

Subtract $1$ from $- 7$ .

$- 2 y = - 8$

$x = \frac{1}{3} - \frac{5 y}{6}$

$- 2 y = - 8$

$x = \frac{1}{3} - \frac{5 y}{6}$

Divide each term in $- 2 y = - 8$ by $- 2$ and simplify.

Divide each term in $- 2 y = - 8$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 8}{- 2}$

$x = \frac{1}{3} - \frac{5 y}{6}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 8}{- 2}$

$x = \frac{1}{3} - \frac{5 y}{6}$

Divide $y$ by $1$ .

$y = \frac{- 8}{- 2}$

$x = \frac{1}{3} - \frac{5 y}{6}$

$y = \frac{- 8}{- 2}$

$x = \frac{1}{3} - \frac{5 y}{6}$

$y = \frac{- 8}{- 2}$

$x = \frac{1}{3} - \frac{5 y}{6}$

Simplify the right side.

Divide $- 8$ by $- 2$ .

$y = 4$

$x = \frac{1}{3} - \frac{5 y}{6}$

$y = 4$

$x = \frac{1}{3} - \frac{5 y}{6}$

$y = 4$

$x = \frac{1}{3} - \frac{5 y}{6}$

$y = 4$

$x = \frac{1}{3} - \frac{5 y}{6}$

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

Replace all occurrences of $y$ in $x = \frac{1}{3} - \frac{5 y}{6}$ with $4$ .

$x = \frac{1}{3} - \frac{5 (4)}{6}$

$y = 4$

Simplify the right side.

Simplify $\frac{1}{3} - \frac{5 (4)}{6}$ .

Simplify each term.

Cancel the common factor of $4$ and $6$ .

Factor $2$ out of $5 (4)$ .

$x = \frac{1}{3} - \frac{2 (5 \cdot (2))}{6}$

$y = 4$

Cancel the common factors.

Factor $2$ out of $6$ .

$x = \frac{1}{3} - \frac{2 (5 \cdot (2))}{2 (3)}$

$y = 4$

Cancel the common factor.

$x = \frac{1}{3} - \frac{2 (5 \cdot (2))}{2 \cdot 3}$

$y = 4$

Rewrite the expression.

$x = \frac{1}{3} - \frac{5 \cdot (2)}{3}$

$y = 4$

$x = \frac{1}{3} - \frac{5 \cdot (2)}{3}$

$y = 4$

$x = \frac{1}{3} - \frac{5 \cdot (2)}{3}$

$y = 4$

Multiply $5$ by $2$ .

$x = \frac{1}{3} - \frac{10}{3}$

$y = 4$

$x = \frac{1}{3} - \frac{10}{3}$

$y = 4$

Combine fractions.

Combine the numerators over the common denominator.

$x = \frac{1 - 10}{3}$

$y = 4$

Simplify the expression.

Subtract $10$ from $1$ .

$x = \frac{- 9}{3}$

$y = 4$

Divide $- 9$ by $3$ .

$x = - 3$

$y = 4$

$x = - 3$

$y = 4$

$x = - 3$

$y = 4$

$x = - 3$

$y = 4$

$x = - 3$

$y = 4$

$x = - 3$

$y = 4$

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

$(- 3, 4)$

The result can be shown in multiple forms.

Point Form:

$(- 3, 4)$

Equation Form:

$x = - 3, y = 4$

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