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

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

Step 1

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

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

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

$y = 2 x + 2$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

$3 x - (2 x) - 1 \cdot 2 = 3$

$y = 2 x + 2$

Multiply $2$ by $- 1$ .

$3 x - 2 x - 1 \cdot 2 = 3$

$y = 2 x + 2$

Multiply $- 1$ by $2$ .

$3 x - 2 x - 2 = 3$

$y = 2 x + 2$

$3 x - 2 x - 2 = 3$

$y = 2 x + 2$

Subtract $2 x$ from $3 x$ .

$x - 2 = 3$

$y = 2 x + 2$

$x - 2 = 3$

$y = 2 x + 2$

$x - 2 = 3$

$y = 2 x + 2$

$x - 2 = 3$

$y = 2 x + 2$

Step 2

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

Add $2$ to both sides of the equation.

$x = 3 + 2$

$y = 2 x + 2$

Add $3$ and $2$ .

$x = 5$

$y = 2 x + 2$

$x = 5$

$y = 2 x + 2$

Step 3

Replace all occurrences of $x$ with $5$ in each equation.

Replace all occurrences of $x$ in $y = 2 x + 2$ with $5$ .

$y = 2 (5) + 2$

$x = 5$

Simplify the right side.

Simplify $2 (5) + 2$ .

Multiply $2$ by $5$ .

$y = 10 + 2$

$x = 5$

Add $10$ and $2$ .

$y = 12$

$x = 5$

$y = 12$

$x = 5$

$y = 12$

$x = 5$

$y = 12$

$x = 5$

Step 4

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

$(5, 12)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(5, 12)$

Equation Form:

$x = 5, y = 12$

Step 6

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

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