Solve the System of Equations x-3y=1 and 2x+2y=18

$x - 3 y = 1$ and $2 x + 2 y = 18$

Step 1

Add $3 y$ to both sides of the equation.

$x = 1 + 3 y$

$2 x + 2 y = 18$

Step 2

Replace all occurrences of $x$ with $1 + 3 y$ in each equation.

Replace all occurrences of $x$ in $2 x + 2 y = 18$ with $1 + 3 y$ .

$2 (1 + 3 y) + 2 y = 18$

$x = 1 + 3 y$

Simplify the left side.

Simplify $2 (1 + 3 y) + 2 y$ .

Simplify each term.

Apply the distributive property.

$2 \cdot 1 + 2 (3 y) + 2 y = 18$

$x = 1 + 3 y$

Multiply $2$ by $1$ .

$2 + 2 (3 y) + 2 y = 18$

$x = 1 + 3 y$

Multiply $3$ by $2$ .

$2 + 6 y + 2 y = 18$

$x = 1 + 3 y$

$2 + 6 y + 2 y = 18$

$x = 1 + 3 y$

Add $6 y$ and $2 y$ .

$2 + 8 y = 18$

$x = 1 + 3 y$

$2 + 8 y = 18$

$x = 1 + 3 y$

$2 + 8 y = 18$

$x = 1 + 3 y$

$2 + 8 y = 18$

$x = 1 + 3 y$

Step 3

Solve for $y$ in $2 + 8 y = 18$ .

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

Subtract $2$ from both sides of the equation.

$8 y = 18 - 2$

$x = 1 + 3 y$

Subtract $2$ from $18$ .

$8 y = 16$

$x = 1 + 3 y$

$8 y = 16$

$x = 1 + 3 y$

Divide each term in $8 y = 16$ by $8$ and simplify.

Divide each term in $8 y = 16$ by $8$ .

$\frac{8 y}{8} = \frac{16}{8}$

$x = 1 + 3 y$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 y}{8} = \frac{16}{8}$

$x = 1 + 3 y$

Divide $y$ by $1$ .

$y = \frac{16}{8}$

$x = 1 + 3 y$

$y = \frac{16}{8}$

$x = 1 + 3 y$

$y = \frac{16}{8}$

$x = 1 + 3 y$

Simplify the right side.

Divide $16$ by $8$ .

$y = 2$

$x = 1 + 3 y$

$y = 2$

$x = 1 + 3 y$

$y = 2$

$x = 1 + 3 y$

$y = 2$

$x = 1 + 3 y$

Step 4

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

Replace all occurrences of $y$ in $x = 1 + 3 y$ with $2$ .

$x = 1 + 3 (2)$

$y = 2$

Simplify the right side.

Simplify $1 + 3 (2)$ .

Multiply $3$ by $2$ .

$x = 1 + 6$

$y = 2$

Add $1$ and $6$ .

$x = 7$

$y = 2$

$x = 7$

$y = 2$

$x = 7$

$y = 2$

$x = 7$

$y = 2$

Step 5

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

$(7, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(7, 2)$

Equation Form:

$x = 7, y = 2$

Step 7

Solve the System of Equations x-3y=1 and 2x+2y=18

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