Solve by Substitution x=8-2y y-x=4

$x = 8 - 2 y$ $y - x = 4$

Step 1

Reorder $8$ and $- 2 y$ .

$x = - 2 y + 8$

$y - x = 4$

Step 2

Replace all occurrences of $x$ with $- 2 y + 8$ in each equation.

Replace all occurrences of $x$ in $y - x = 4$ with $- 2 y + 8$ .

$y - (- 2 y + 8) = 4$

$x = - 2 y + 8$

Simplify the left side.

Simplify $y - (- 2 y + 8)$ .

Simplify each term.

Apply the distributive property.

$y - (- 2 y) - 1 \cdot 8 = 4$

$x = - 2 y + 8$

Multiply $- 2$ by $- 1$ .

$y + 2 y - 1 \cdot 8 = 4$

$x = - 2 y + 8$

Multiply $- 1$ by $8$ .

$y + 2 y - 8 = 4$

$x = - 2 y + 8$

$y + 2 y - 8 = 4$

$x = - 2 y + 8$

Add $y$ and $2 y$ .

$3 y - 8 = 4$

$x = - 2 y + 8$

$3 y - 8 = 4$

$x = - 2 y + 8$

$3 y - 8 = 4$

$x = - 2 y + 8$

$3 y - 8 = 4$

$x = - 2 y + 8$

Step 3

Solve for $y$ in $3 y - 8 = 4$ .

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

Add $8$ to both sides of the equation.

$3 y = 4 + 8$

$x = - 2 y + 8$

Add $4$ and $8$ .

$3 y = 12$

$x = - 2 y + 8$

$3 y = 12$

$x = - 2 y + 8$

Divide each term in $3 y = 12$ by $3$ and simplify.

Divide each term in $3 y = 12$ by $3$ .

$\frac{3 y}{3} = \frac{12}{3}$

$x = - 2 y + 8$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{12}{3}$

$x = - 2 y + 8$

Divide $y$ by $1$ .

$y = \frac{12}{3}$

$x = - 2 y + 8$

$y = \frac{12}{3}$

$x = - 2 y + 8$

$y = \frac{12}{3}$

$x = - 2 y + 8$

Simplify the right side.

Divide $12$ by $3$ .

$y = 4$

$x = - 2 y + 8$

$y = 4$

$x = - 2 y + 8$

$y = 4$

$x = - 2 y + 8$

$y = 4$

$x = - 2 y + 8$

Step 4

Replace all occurrences of $y$ with $4$ in each equation.

Replace all occurrences of $y$ in $x = - 2 y + 8$ with $4$ .

$x = - 2 \cdot 4 + 8$

$y = 4$

Simplify the right side.

Simplify $- 2 \cdot 4 + 8$ .

Multiply $- 2$ by $4$ .

$x = - 8 + 8$

$y = 4$

Add $- 8$ and $8$ .

$x = 0$

$y = 4$

$x = 0$

$y = 4$

$x = 0$

$y = 4$

$x = 0$

$y = 4$

Step 5

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

$(0, 4)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(0, 4)$

Equation Form:

$x = 0, y = 4$

Step 7

Solve by Substitution x=8-2y y-x=4

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