Solve by Substitution y=2-6x , 1/2y-x=1

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

Step 1

Reorder $2$ and $- 6 x$ .

$y = - 6 x + 2$

$\frac{1}{2} y - x = 1$

Step 2

Replace all occurrences of $y$ with $- 6 x + 2$ in each equation.

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

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

$y = - 6 x + 2$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

$y = - 6 x + 2$

Cancel the common factor of $2$ .

Factor $2$ out of $- 6 x$ .

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

$y = - 6 x + 2$

Cancel the common factor.

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

$y = - 6 x + 2$

Rewrite the expression.

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

$y = - 6 x + 2$

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

$y = - 6 x + 2$

Cancel the common factor of $2$ .

Cancel the common factor.

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

$y = - 6 x + 2$

Rewrite the expression.

$- 3 x + 1 - x = 1$

$y = - 6 x + 2$

$- 3 x + 1 - x = 1$

$y = - 6 x + 2$

$- 3 x + 1 - x = 1$

$y = - 6 x + 2$

Subtract $x$ from $- 3 x$ .

$- 4 x + 1 = 1$

$y = - 6 x + 2$

$- 4 x + 1 = 1$

$y = - 6 x + 2$

$- 4 x + 1 = 1$

$y = - 6 x + 2$

$- 4 x + 1 = 1$

$y = - 6 x + 2$

Step 3

Solve for $x$ in $- 4 x + 1 = 1$ .

Move all terms not containing $x$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$- 4 x = 1 - 1$

$y = - 6 x + 2$

Subtract $1$ from $1$ .

$- 4 x = 0$

$y = - 6 x + 2$

$- 4 x = 0$

$y = - 6 x + 2$

Divide each term in $- 4 x = 0$ by $- 4$ and simplify.

Divide each term in $- 4 x = 0$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{0}{- 4}$

$y = - 6 x + 2$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{0}{- 4}$

$y = - 6 x + 2$

Divide $x$ by $1$ .

$x = \frac{0}{- 4}$

$y = - 6 x + 2$

$x = \frac{0}{- 4}$

$y = - 6 x + 2$

$x = \frac{0}{- 4}$

$y = - 6 x + 2$

Simplify the right side.

Divide $0$ by $- 4$ .

$x = 0$

$y = - 6 x + 2$

$x = 0$

$y = - 6 x + 2$

$x = 0$

$y = - 6 x + 2$

$x = 0$

$y = - 6 x + 2$

Step 4

Replace all occurrences of $x$ with $0$ in each equation.

Replace all occurrences of $x$ in $y = - 6 x + 2$ with $0$ .

$y = - 6 \cdot 0 + 2$

$x = 0$

Simplify the right side.

Simplify $- 6 \cdot 0 + 2$ .

Multiply $- 6$ by $0$ .

$y = 0 + 2$

$x = 0$

Add $0$ and $2$ .

$y = 2$

$x = 0$

$y = 2$

$x = 0$

$y = 2$

$x = 0$

$y = 2$

$x = 0$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(0, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(0, 2)$

Equation Form:

$x = 0, y = 2$

Step 7

Solve by Substitution y=2-6x , 1/2y-x=1

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