Solve the System of Equations 3x=3+y -3x+y=-3

$3 x = 3 + y$ $- 3 x + y = - 3$

Step 1

Divide each term in $3 x = 3 + y$ by $3$ and simplify.

Divide each term in $3 x = 3 + y$ by $3$ .

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

$- 3 x + y = - 3$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

$- 3 x + y = - 3$

Divide $x$ by $1$ .

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

$- 3 x + y = - 3$

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

$- 3 x + y = - 3$

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

$- 3 x + y = - 3$

Simplify the right side.

Divide $3$ by $3$ .

$x = 1 + \frac{y}{3}$

$- 3 x + y = - 3$

$x = 1 + \frac{y}{3}$

$- 3 x + y = - 3$

$x = 1 + \frac{y}{3}$

$- 3 x + y = - 3$

Step 2

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

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

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

$x = 1 + \frac{y}{3}$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

$- 3 \cdot 1 - 3 \frac{y}{3} + y = - 3$

$x = 1 + \frac{y}{3}$

Multiply $- 3$ by $1$ .

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

$x = 1 + \frac{y}{3}$

Cancel the common factor of $3$ .

Factor $3$ out of $- 3$ .

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

$x = 1 + \frac{y}{3}$

Cancel the common factor.

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

$x = 1 + \frac{y}{3}$

Rewrite the expression.

$- 3 - 1 y + y = - 3$

$x = 1 + \frac{y}{3}$

$- 3 - 1 y + y = - 3$

$x = 1 + \frac{y}{3}$

Rewrite $- 1 y$ as $- y$ .

$- 3 - y + y = - 3$

$x = 1 + \frac{y}{3}$

$- 3 - y + y = - 3$

$x = 1 + \frac{y}{3}$

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

Add $- y$ and $y$ .

$- 3 + 0 = - 3$

$x = 1 + \frac{y}{3}$

Add $- 3$ and $0$ .

$- 3 = - 3$

$x = 1 + \frac{y}{3}$

$- 3 = - 3$

$x = 1 + \frac{y}{3}$

$- 3 = - 3$

$x = 1 + \frac{y}{3}$

$- 3 = - 3$

$x = 1 + \frac{y}{3}$

$- 3 = - 3$

$x = 1 + \frac{y}{3}$

Step 3

Remove any equations from the system that are always true.

$x = 1 + \frac{y}{3}$

Step 4

Solve the System of Equations 3x=3+y -3x+y=-3

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