Solve by Substitution 2x-3y=1 x+3y=5

$2 x - 3 y = 1$ $x + 3 y = 5$

Step 1

Subtract $3 y$ from both sides of the equation.

$x = 5 - 3 y$

$2 x - 3 y = 1$

Step 2

Replace all occurrences of $x$ with $5 - 3 y$ in each equation.

Replace all occurrences of $x$ in $2 x - 3 y = 1$ with $5 - 3 y$ .

$2 (5 - 3 y) - 3 y = 1$

$x = 5 - 3 y$

Simplify the left side.

Simplify $2 (5 - 3 y) - 3 y$ .

Simplify each term.

Apply the distributive property.

$2 \cdot 5 + 2 (- 3 y) - 3 y = 1$

$x = 5 - 3 y$

Multiply $2$ by $5$ .

$10 + 2 (- 3 y) - 3 y = 1$

$x = 5 - 3 y$

Multiply $- 3$ by $2$ .

$10 - 6 y - 3 y = 1$

$x = 5 - 3 y$

$10 - 6 y - 3 y = 1$

$x = 5 - 3 y$

Subtract $3 y$ from $- 6 y$ .

$10 - 9 y = 1$

$x = 5 - 3 y$

$10 - 9 y = 1$

$x = 5 - 3 y$

$10 - 9 y = 1$

$x = 5 - 3 y$

$10 - 9 y = 1$

$x = 5 - 3 y$

Step 3

Solve for $y$ in $10 - 9 y = 1$ .

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

Subtract $10$ from both sides of the equation.

$- 9 y = 1 - 10$

$x = 5 - 3 y$

Subtract $10$ from $1$ .

$- 9 y = - 9$

$x = 5 - 3 y$

$- 9 y = - 9$

$x = 5 - 3 y$

Divide each term in $- 9 y = - 9$ by $- 9$ and simplify.

Divide each term in $- 9 y = - 9$ by $- 9$ .

$\frac{- 9 y}{- 9} = \frac{- 9}{- 9}$

$x = 5 - 3 y$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 y}{- 9} = \frac{- 9}{- 9}$

$x = 5 - 3 y$

Divide $y$ by $1$ .

$y = \frac{- 9}{- 9}$

$x = 5 - 3 y$

$y = \frac{- 9}{- 9}$

$x = 5 - 3 y$

$y = \frac{- 9}{- 9}$

$x = 5 - 3 y$

Simplify the right side.

Divide $- 9$ by $- 9$ .

$y = 1$

$x = 5 - 3 y$

$y = 1$

$x = 5 - 3 y$

$y = 1$

$x = 5 - 3 y$

$y = 1$

$x = 5 - 3 y$

Step 4

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

Replace all occurrences of $y$ in $x = 5 - 3 y$ with $1$ .

$x = 5 - 3 \cdot 1$

$y = 1$

Simplify the right side.

Simplify $5 - 3 \cdot 1$ .

Multiply $- 3$ by $1$ .

$x = 5 - 3$

$y = 1$

Subtract $3$ from $5$ .

$x = 2$

$y = 1$

$x = 2$

$y = 1$

$x = 2$

$y = 1$

$x = 2$

$y = 1$

Step 5

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

$(2, 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(2, 1)$

Equation Form:

$x = 2, y = 1$

Step 7

Solve by Substitution 2x-3y=1 x+3y=5

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