Solve the System of Equations 2x-6y=30 y=1/3x+1

$2 x - 6 y = 30$ $y = \frac{1}{3} x + 1$

Step 1

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

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

$2 x - 6 y = 30$

Step 2

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

Replace all occurrences of $y$ in $2 x - 6 y = 30$ with $\frac{x}{3} + 1$ .

$2 x - 6 (\frac{x}{3} + 1) = 30$

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

Simplify the left side.

Simplify $2 x - 6 (\frac{x}{3} + 1)$ .

Simplify each term.

Apply the distributive property.

$2 x - 6 \frac{x}{3} - 6 \cdot 1 = 30$

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

Cancel the common factor of $3$ .

Factor $3$ out of $- 6$ .

$2 x + 3 (- 2) (\frac{x}{3}) - 6 \cdot 1 = 30$

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

Cancel the common factor.

$2 x + 3 \cdot (- 2 \frac{x}{3}) - 6 \cdot 1 = 30$

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

Rewrite the expression.

$2 x - 2 x - 6 \cdot 1 = 30$

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

$2 x - 2 x - 6 \cdot 1 = 30$

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

Multiply $- 6$ by $1$ .

$2 x - 2 x - 6 = 30$

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

$2 x - 2 x - 6 = 30$

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

Simplify by adding terms.

Subtract $2 x$ from $2 x$ .

$0 - 6 = 30$

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

Subtract $6$ from $0$ .

$- 6 = 30$

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

$- 6 = 30$

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

$- 6 = 30$

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

$- 6 = 30$

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

$- 6 = 30$

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

Step 3

Since $- 6 = 30$ is not true, there is no solution.

No solution

Step 4

Solve the System of Equations 2x-6y=30 y=1/3x+1

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