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

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

Step 1

Replace all occurrences of $y$ with $3 x + 3$ in each equation.

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

$2 (3 x + 3) - 2 x = 6$

$y = 3 x + 3$

Simplify the left side.

Simplify $2 (3 x + 3) - 2 x$ .

Simplify each term.

Apply the distributive property.

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

$y = 3 x + 3$

Multiply $3$ by $2$ .

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

$y = 3 x + 3$

Multiply $2$ by $3$ .

$6 x + 6 - 2 x = 6$

$y = 3 x + 3$

$6 x + 6 - 2 x = 6$

$y = 3 x + 3$

Subtract $2 x$ from $6 x$ .

$4 x + 6 = 6$

$y = 3 x + 3$

$4 x + 6 = 6$

$y = 3 x + 3$

$4 x + 6 = 6$

$y = 3 x + 3$

$4 x + 6 = 6$

$y = 3 x + 3$

Step 2

Solve for $x$ in $4 x + 6 = 6$ .

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

Subtract $6$ from both sides of the equation.

$4 x = 6 - 6$

$y = 3 x + 3$

Subtract $6$ from $6$ .

$4 x = 0$

$y = 3 x + 3$

$4 x = 0$

$y = 3 x + 3$

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

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

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

$y = 3 x + 3$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

$y = 3 x + 3$

Divide $x$ by $1$ .

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

$y = 3 x + 3$

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

$y = 3 x + 3$

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

$y = 3 x + 3$

Simplify the right side.

Divide $0$ by $4$ .

$x = 0$

$y = 3 x + 3$

$x = 0$

$y = 3 x + 3$

$x = 0$

$y = 3 x + 3$

$x = 0$

$y = 3 x + 3$

Step 3

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

Replace all occurrences of $x$ in $y = 3 x + 3$ with $0$ .

$y = 3 (0) + 3$

$x = 0$

Simplify the right side.

Simplify $3 (0) + 3$ .

Multiply $3$ by $0$ .

$y = 0 + 3$

$x = 0$

Add $0$ and $3$ .

$y = 3$

$x = 0$

$y = 3$

$x = 0$

$y = 3$

$x = 0$

$y = 3$

$x = 0$

Step 4

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

$(0, 3)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(0, 3)$

Equation Form:

$x = 0, y = 3$

Step 6

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

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