Solve the System of Equations 3x+7y=23 -3x-7y=-17

$3 x + 7 y = 23$ $- 3 x - 7 y = - 17$

Step 1

Solve for $x$ in $3 x + 7 y = 23$ .

Subtract $7 y$ from both sides of the equation.

$3 x = 23 - 7 y$

$- 3 x - 7 y = - 17$

Divide each term in $3 x = 23 - 7 y$ by $3$ and simplify.

Divide each term in $3 x = 23 - 7 y$ by $3$ .

$\frac{3 x}{3} = \frac{23}{3} + \frac{- 7 y}{3}$

$- 3 x - 7 y = - 17$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{23}{3} + \frac{- 7 y}{3}$

$- 3 x - 7 y = - 17$

Divide $x$ by $1$ .

$x = \frac{23}{3} + \frac{- 7 y}{3}$

$- 3 x - 7 y = - 17$

$x = \frac{23}{3} + \frac{- 7 y}{3}$

$- 3 x - 7 y = - 17$

$x = \frac{23}{3} + \frac{- 7 y}{3}$

$- 3 x - 7 y = - 17$

Simplify the right side.

Move the negative in front of the fraction.

$x = \frac{23}{3} - \frac{7 y}{3}$

$- 3 x - 7 y = - 17$

$x = \frac{23}{3} - \frac{7 y}{3}$

$- 3 x - 7 y = - 17$

$x = \frac{23}{3} - \frac{7 y}{3}$

$- 3 x - 7 y = - 17$

$x = \frac{23}{3} - \frac{7 y}{3}$

$- 3 x - 7 y = - 17$

Step 2

Replace all occurrences of $x$ with $\frac{23}{3} - \frac{7 y}{3}$ in each equation.

Replace all occurrences of $x$ in $- 3 x - 7 y = - 17$ with $\frac{23}{3} - \frac{7 y}{3}$ .

$- 3 (\frac{23}{3} - \frac{7 y}{3}) - 7 y = - 17$

$x = \frac{23}{3} - \frac{7 y}{3}$

Simplify the left side.

Simplify $- 3 (\frac{23}{3} - \frac{7 y}{3}) - 7 y$ .

Simplify each term.

Apply the distributive property.

$- 3 (\frac{23}{3}) - 3 (- \frac{7 y}{3}) - 7 y = - 17$

$x = \frac{23}{3} - \frac{7 y}{3}$

Cancel the common factor of $3$ .

Factor $3$ out of $- 3$ .

$3 (- 1) (\frac{23}{3}) - 3 (- \frac{7 y}{3}) - 7 y = - 17$

$x = \frac{23}{3} - \frac{7 y}{3}$

Cancel the common factor.

$3 \cdot (- 1 (\frac{23}{3})) - 3 (- \frac{7 y}{3}) - 7 y = - 17$

$x = \frac{23}{3} - \frac{7 y}{3}$

Rewrite the expression.

$- 1 \cdot 23 - 3 (- \frac{7 y}{3}) - 7 y = - 17$

$x = \frac{23}{3} - \frac{7 y}{3}$

$- 1 \cdot 23 - 3 (- \frac{7 y}{3}) - 7 y = - 17$

$x = \frac{23}{3} - \frac{7 y}{3}$

Multiply $- 1$ by $23$ .

$- 23 - 3 (- \frac{7 y}{3}) - 7 y = - 17$

$x = \frac{23}{3} - \frac{7 y}{3}$

Cancel the common factor of $3$ .

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

$- 23 - 3 \frac{- 7 y}{3} - 7 y = - 17$

$x = \frac{23}{3} - \frac{7 y}{3}$

Factor $3$ out of $- 3$ .

$- 23 + 3 (- 1) (\frac{- 7 y}{3}) - 7 y = - 17$

$x = \frac{23}{3} - \frac{7 y}{3}$

Cancel the common factor.

$- 23 + 3 \cdot (- 1 \frac{- 7 y}{3}) - 7 y = - 17$

$x = \frac{23}{3} - \frac{7 y}{3}$

Rewrite the expression.

$- 23 - 1 (- 7 y) - 7 y = - 17$

$x = \frac{23}{3} - \frac{7 y}{3}$

$- 23 - 1 (- 7 y) - 7 y = - 17$

$x = \frac{23}{3} - \frac{7 y}{3}$

Multiply $- 7$ by $- 1$ .

$- 23 + 7 y - 7 y = - 17$

$x = \frac{23}{3} - \frac{7 y}{3}$

$- 23 + 7 y - 7 y = - 17$

$x = \frac{23}{3} - \frac{7 y}{3}$

Combine the opposite terms in $- 23 + 7 y - 7 y$ .

Subtract $7 y$ from $7 y$ .

$- 23 + 0 = - 17$

$x = \frac{23}{3} - \frac{7 y}{3}$

Add $- 23$ and $0$ .

$- 23 = - 17$

$x = \frac{23}{3} - \frac{7 y}{3}$

$- 23 = - 17$

$x = \frac{23}{3} - \frac{7 y}{3}$

$- 23 = - 17$

$x = \frac{23}{3} - \frac{7 y}{3}$

$- 23 = - 17$

$x = \frac{23}{3} - \frac{7 y}{3}$

$- 23 = - 17$

$x = \frac{23}{3} - \frac{7 y}{3}$

Step 3

Since $- 23 = - 17$ is not true, there is no solution.

No solution

Step 4

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