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

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

Step 1

Combine $\frac{1}{3}$ and $x$ .

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

$- x + 3 y = 6$

Step 2

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

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

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

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

Simplify the left side.

Simplify $- x + 3 (\frac{x}{3} + 2)$ .

Simplify each term.

Apply the distributive property.

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

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

Rewrite the expression.

$- x + x + 3 \cdot 2 = 6$

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

$- x + x + 3 \cdot 2 = 6$

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

Multiply $3$ by $2$ .

$- x + x + 6 = 6$

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

$- x + x + 6 = 6$

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

Simplify by adding terms.

Add $- x$ and $x$ .

$0 + 6 = 6$

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

Add $0$ and $6$ .

$6 = 6$

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

$6 = 6$

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

$6 = 6$

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

$6 = 6$

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

$6 = 6$

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

Step 3

Remove any equations from the system that are always true.

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

Step 4

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

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