Solve by Substitution x-2y=2 , 3x+y=6

$x - 2 y = 2$ , $3 x + y = 6$

Step 1

Add $2 y$ to both sides of the equation.

$x = 2 + 2 y$

$3 x + y = 6$

Step 2

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

Replace all occurrences of $x$ in $3 x + y = 6$ with $2 + 2 y$ .

$3 (2 + 2 y) + y = 6$

$x = 2 + 2 y$

Simplify the left side.

Simplify $3 (2 + 2 y) + y$ .

Simplify each term.

Apply the distributive property.

$3 \cdot 2 + 3 (2 y) + y = 6$

$x = 2 + 2 y$

Multiply $3$ by $2$ .

$6 + 3 (2 y) + y = 6$

$x = 2 + 2 y$

Multiply $2$ by $3$ .

$6 + 6 y + y = 6$

$x = 2 + 2 y$

$6 + 6 y + y = 6$

$x = 2 + 2 y$

Add $6 y$ and $y$ .

$6 + 7 y = 6$

$x = 2 + 2 y$

$6 + 7 y = 6$

$x = 2 + 2 y$

$6 + 7 y = 6$

$x = 2 + 2 y$

$6 + 7 y = 6$

$x = 2 + 2 y$

Step 3

Solve for $y$ in $6 + 7 y = 6$ .

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

Subtract $6$ from both sides of the equation.

$7 y = 6 - 6$

$x = 2 + 2 y$

Subtract $6$ from $6$ .

$7 y = 0$

$x = 2 + 2 y$

$7 y = 0$

$x = 2 + 2 y$

Divide each term in $7 y = 0$ by $7$ and simplify.

Divide each term in $7 y = 0$ by $7$ .

$\frac{7 y}{7} = \frac{0}{7}$

$x = 2 + 2 y$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{0}{7}$

$x = 2 + 2 y$

Divide $y$ by $1$ .

$y = \frac{0}{7}$

$x = 2 + 2 y$

$y = \frac{0}{7}$

$x = 2 + 2 y$

$y = \frac{0}{7}$

$x = 2 + 2 y$

Simplify the right side.

Divide $0$ by $7$ .

$y = 0$

$x = 2 + 2 y$

$y = 0$

$x = 2 + 2 y$

$y = 0$

$x = 2 + 2 y$

$y = 0$

$x = 2 + 2 y$

Step 4

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

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

$x = 2 + 2 (0)$

$y = 0$

Simplify the right side.

Simplify $2 + 2 (0)$ .

Multiply $2$ by $0$ .

$x = 2 + 0$

$y = 0$

Add $2$ and $0$ .

$x = 2$

$y = 0$

$x = 2$

$y = 0$

$x = 2$

$y = 0$

$x = 2$

$y = 0$

Step 5

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

$(2, 0)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(2, 0)$

Equation Form:

$x = 2, y = 0$

Step 7

Solve by Substitution x-2y=2 , 3x+y=6

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