Solve the System of Equations x+y=5 2x-y=4

$x + y = 5$ $2 x - y = 4$

Subtract $y$ from both sides of the equation.

$x = 5 - y$

$2 x - y = 4$

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

Replace all occurrences of $x$ in $2 x - y = 4$ with $5 - y$ .

$2 (5 - y) - y = 4$

$x = 5 - y$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

$2 \cdot 5 + 2 (- y) - y = 4$

$x = 5 - y$

Multiply $2$ by $5$ .

$10 + 2 (- y) - y = 4$

$x = 5 - y$

Multiply $- 1$ by $2$ .

$10 - 2 y - y = 4$

$x = 5 - y$

$10 - 2 y - y = 4$

$x = 5 - y$

Subtract $y$ from $- 2 y$ .

$10 - 3 y = 4$

$x = 5 - y$

$10 - 3 y = 4$

$x = 5 - y$

$10 - 3 y = 4$

$x = 5 - y$

$10 - 3 y = 4$

$x = 5 - y$

Solve for $y$ in $10 - 3 y = 4$ .

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

Subtract $10$ from both sides of the equation.

$- 3 y = 4 - 10$

$x = 5 - y$

Subtract $10$ from $4$ .

$- 3 y = - 6$

$x = 5 - y$

$- 3 y = - 6$

$x = 5 - y$

Divide each term in $- 3 y = - 6$ by $- 3$ and simplify.

Divide each term in $- 3 y = - 6$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 6}{- 3}$

$x = 5 - y$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 6}{- 3}$

$x = 5 - y$

Divide $y$ by $1$ .

$y = \frac{- 6}{- 3}$

$x = 5 - y$

$y = \frac{- 6}{- 3}$

$x = 5 - y$

$y = \frac{- 6}{- 3}$

$x = 5 - y$

Simplify the right side.

Divide $- 6$ by $- 3$ .

$y = 2$

$x = 5 - y$

$y = 2$

$x = 5 - y$

$y = 2$

$x = 5 - y$

$y = 2$

$x = 5 - y$

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

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

$x = 5 - (2)$

$y = 2$

Simplify the right side.

Simplify $5 - (2)$ .

Multiply $- 1$ by $2$ .

$x = 5 - 2$

$y = 2$

Subtract $2$ from $5$ .

$x = 3$

$y = 2$

$x = 3$

$y = 2$

$x = 3$

$y = 2$

$x = 3$

$y = 2$

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

$(3, 2)$

The result can be shown in multiple forms.

Point Form:

$(3, 2)$

Equation Form:

$x = 3, y = 2$

Solve the System of Equations x+y=5 2x-y=4

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