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

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

Eliminate the equal sides of each equation and combine.

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

Solve $- \frac{3}{2} x - 7 = \frac{5}{6} x + 7$ for $x$ .

Simplify each term.

Combine $x$ and $\frac{3}{2}$ .

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

Move $3$ to the left of $x$ .

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

Combine $\frac{5}{6}$ and $x$ .

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

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

Subtract $\frac{5 x}{6}$ from both sides of the equation.

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

To write $- \frac{3 x}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{3 x}{2} \cdot \frac{3}{3} - \frac{5 x}{6} - 7 = 7$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 x}{2}$ by $\frac{3}{3}$ .

$- \frac{3 x \cdot 3}{2 \cdot 3} - \frac{5 x}{6} - 7 = 7$

Multiply $2$ by $3$ .

$- \frac{3 x \cdot 3}{6} - \frac{5 x}{6} - 7 = 7$

Combine the numerators over the common denominator.

$\frac{- 3 x \cdot 3 - 5 x}{6} - 7 = 7$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- 3 x \cdot 3 - 5 x$ .

Factor $x$ out of $- 3 x \cdot 3$ .

$\frac{x (- 3 \cdot 3) - 5 x}{6} - 7 = 7$

Factor $x$ out of $- 5 x$ .

$\frac{x (- 3 \cdot 3) + x \cdot - 5}{6} - 7 = 7$

Factor $x$ out of $x (- 3 \cdot 3) + x \cdot - 5$ .

$\frac{x (- 3 \cdot 3 - 5)}{6} - 7 = 7$

Multiply $- 3$ by $3$ .

$\frac{x (- 9 - 5)}{6} - 7 = 7$

Subtract $5$ from $- 9$ .

$\frac{x \cdot - 14}{6} - 7 = 7$

Cancel the common factor of $- 14$ and $6$ .

Factor $2$ out of $x \cdot - 14$ .

$\frac{2 (x \cdot - 7)}{6} - 7 = 7$

Cancel the common factors.

Factor $2$ out of $6$ .

$\frac{2 (x \cdot - 7)}{2 (3)} - 7 = 7$

Cancel the common factor.

$\frac{2 (x \cdot - 7)}{2 \cdot 3} - 7 = 7$

Rewrite the expression.

$\frac{x \cdot - 7}{3} - 7 = 7$

Move $- 7$ to the left of $x$ .

$\frac{- 7 \cdot x}{3} - 7 = 7$

Move the negative in front of the fraction.

$- \frac{7 x}{3} - 7 = 7$

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

Add $7$ to both sides of the equation.

$- \frac{7 x}{3} = 7 + 7$

Add $7$ and $7$ .

$- \frac{7 x}{3} = 14$

Multiply both sides of the equation by $- \frac{3}{7}$ .

$- \frac{3}{7} (- \frac{7 x}{3}) = - \frac{3}{7} \cdot 14$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{3}{7} (- \frac{7 x}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{7}$ into the numerator.

$\frac{- 3}{7} (- \frac{7 x}{3}) = - \frac{3}{7} \cdot 14$

Move the leading negative in $- \frac{7 x}{3}$ into the numerator.

$\frac{- 3}{7} \cdot \frac{- 7 x}{3} = - \frac{3}{7} \cdot 14$

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{7} \cdot \frac{- 7 x}{3} = - \frac{3}{7} \cdot 14$

Cancel the common factor.

$\frac{3 \cdot - 1}{7} \cdot \frac{- 7 x}{3} = - \frac{3}{7} \cdot 14$

Rewrite the expression.

$\frac{- 1}{7} (- 7 x) = - \frac{3}{7} \cdot 14$

Cancel the common factor of $7$ .

Factor $7$ out of $- 7 x$ .

$\frac{- 1}{7} (7 (- x)) = - \frac{3}{7} \cdot 14$

Cancel the common factor.

$\frac{- 1}{7} (7 (- x)) = - \frac{3}{7} \cdot 14$

Rewrite the expression.

$- - x = - \frac{3}{7} \cdot 14$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{3}{7} \cdot 14$

Multiply $x$ by $1$ .

$x = - \frac{3}{7} \cdot 14$

Simplify the right side.

Simplify $- \frac{3}{7} \cdot 14$ .

Cancel the common factor of $7$ .

Move the leading negative in $- \frac{3}{7}$ into the numerator.

$x = \frac{- 3}{7} \cdot 14$

Factor $7$ out of $14$ .

$x = \frac{- 3}{7} \cdot (7 (2))$

Cancel the common factor.

$x = \frac{- 3}{7} \cdot (7 \cdot 2)$

Rewrite the expression.

$x = - 3 \cdot 2$

Multiply $- 3$ by $2$ .

$x = - 6$

Evaluate $y$ when $x = - 6$ .

Substitute $- 6$ for $x$ .

$y = \frac{5}{6} \cdot (- 6) + 7$

Substitute $- 6$ for $x$ in $y = \frac{5}{6} \cdot (- 6) + 7$ and solve for $y$ .

Multiply $\frac{5}{6}$ by $- 6$ .

$y = \frac{5}{6} \cdot - 6 + 7$

Simplify $\frac{5}{6} \cdot - 6 + 7$ .

Simplify each term.

Cancel the common factor of $6$ .

Factor $6$ out of $- 6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$y = 5 \cdot - 1 + 7$

Multiply $5$ by $- 1$ .

$y = - 5 + 7$

Add $- 5$ and $7$ .

$y = 2$

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

$(- 6, 2)$

The result can be shown in multiple forms.

Point Form:

$(- 6, 2)$

Equation Form:

$x = - 6, y = 2$

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

Related Questions

Support LCMGCF.com by disabling your adblocker.