Solve by Substitution 9x-3y=-21 6x=2y-4

$9 x - 3 y = - 21$ $6 x = 2 y - 4$

Divide each term in $6 x = 2 y - 4$ by $6$ and simplify.

Divide each term in $6 x = 2 y - 4$ by $6$ .

$\frac{6 x}{6} = \frac{2 y}{6} + \frac{- 4}{6}$

$9 x - 3 y = - 21$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{2 y}{6} + \frac{- 4}{6}$

$9 x - 3 y = - 21$

Divide $x$ by $1$ .

$x = \frac{2 y}{6} + \frac{- 4}{6}$

$9 x - 3 y = - 21$

$x = \frac{2 y}{6} + \frac{- 4}{6}$

$9 x - 3 y = - 21$

$x = \frac{2 y}{6} + \frac{- 4}{6}$

$9 x - 3 y = - 21$

Simplify the right side.

Simplify each term.

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

Factor $2$ out of $2 y$ .

$x = \frac{2 (y)}{6} + \frac{- 4}{6}$

$9 x - 3 y = - 21$

Cancel the common factors.

Factor $2$ out of $6$ .

$x = \frac{2 y}{2 \cdot 3} + \frac{- 4}{6}$

$9 x - 3 y = - 21$

Cancel the common factor.

$x = \frac{2 y}{2 \cdot 3} + \frac{- 4}{6}$

$9 x - 3 y = - 21$

Rewrite the expression.

$x = \frac{y}{3} + \frac{- 4}{6}$

$9 x - 3 y = - 21$

$x = \frac{y}{3} + \frac{- 4}{6}$

$9 x - 3 y = - 21$

$x = \frac{y}{3} + \frac{- 4}{6}$

$9 x - 3 y = - 21$

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

Factor $2$ out of $- 4$ .

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

$9 x - 3 y = - 21$

Cancel the common factors.

Factor $2$ out of $6$ .

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

$9 x - 3 y = - 21$

Cancel the common factor.

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

$9 x - 3 y = - 21$

Rewrite the expression.

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

$9 x - 3 y = - 21$

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

$9 x - 3 y = - 21$

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

$9 x - 3 y = - 21$

Move the negative in front of the fraction.

$x = \frac{y}{3} - \frac{2}{3}$

$9 x - 3 y = - 21$

$x = \frac{y}{3} - \frac{2}{3}$

$9 x - 3 y = - 21$

$x = \frac{y}{3} - \frac{2}{3}$

$9 x - 3 y = - 21$

$x = \frac{y}{3} - \frac{2}{3}$

$9 x - 3 y = - 21$

Replace all occurrences of $x$ with $\frac{y}{3} - \frac{2}{3}$ in each equation.

Replace all occurrences of $x$ in $9 x - 3 y = - 21$ with $\frac{y}{3} - \frac{2}{3}$ .

$9 (\frac{y}{3} - \frac{2}{3}) - 3 y = - 21$

$x = \frac{y}{3} - \frac{2}{3}$

Simplify the left side.

Simplify $9 (\frac{y}{3} - \frac{2}{3}) - 3 y$ .

Simplify each term.

Apply the distributive property.

$9 (\frac{y}{3}) + 9 (- \frac{2}{3}) - 3 y = - 21$

$x = \frac{y}{3} - \frac{2}{3}$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$3 (3) (\frac{y}{3}) + 9 (- \frac{2}{3}) - 3 y = - 21$

$x = \frac{y}{3} - \frac{2}{3}$

Cancel the common factor.

$3 \cdot (3 (\frac{y}{3})) + 9 (- \frac{2}{3}) - 3 y = - 21$

$x = \frac{y}{3} - \frac{2}{3}$

Rewrite the expression.

$3 y + 9 (- \frac{2}{3}) - 3 y = - 21$

$x = \frac{y}{3} - \frac{2}{3}$

$3 y + 9 (- \frac{2}{3}) - 3 y = - 21$

$x = \frac{y}{3} - \frac{2}{3}$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$3 y + 9 (\frac{- 2}{3}) - 3 y = - 21$

$x = \frac{y}{3} - \frac{2}{3}$

Factor $3$ out of $9$ .

$3 y + 3 (3) (\frac{- 2}{3}) - 3 y = - 21$

$x = \frac{y}{3} - \frac{2}{3}$

Cancel the common factor.

$3 y + 3 \cdot (3 (\frac{- 2}{3})) - 3 y = - 21$

$x = \frac{y}{3} - \frac{2}{3}$

Rewrite the expression.

$3 y + 3 \cdot - 2 - 3 y = - 21$

$x = \frac{y}{3} - \frac{2}{3}$

$3 y + 3 \cdot - 2 - 3 y = - 21$

$x = \frac{y}{3} - \frac{2}{3}$

Multiply $3$ by $- 2$ .

$3 y - 6 - 3 y = - 21$

$x = \frac{y}{3} - \frac{2}{3}$

$3 y - 6 - 3 y = - 21$

$x = \frac{y}{3} - \frac{2}{3}$

Combine the opposite terms in $3 y - 6 - 3 y$ .

Subtract $3 y$ from $3 y$ .

$0 - 6 = - 21$

$x = \frac{y}{3} - \frac{2}{3}$

Subtract $6$ from $0$ .

$- 6 = - 21$

$x = \frac{y}{3} - \frac{2}{3}$

$- 6 = - 21$

$x = \frac{y}{3} - \frac{2}{3}$

$- 6 = - 21$

$x = \frac{y}{3} - \frac{2}{3}$

$- 6 = - 21$

$x = \frac{y}{3} - \frac{2}{3}$

$- 6 = - 21$

$x = \frac{y}{3} - \frac{2}{3}$

Since $- 6 = - 21$ is not true, there is no solution.

No solution

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