Solve the System of Equations x+y=3 2x+y=2

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

Step 1

Subtract $y$ from both sides of the equation.

$x = 3 - y$

$2 x + y = 2$

Step 2

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

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

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

$x = 3 - y$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

$x = 3 - y$

Multiply $2$ by $3$ .

$6 + 2 (- y) + y = 2$

$x = 3 - y$

Multiply $- 1$ by $2$ .

$6 - 2 y + y = 2$

$x = 3 - y$

$6 - 2 y + y = 2$

$x = 3 - y$

Add $- 2 y$ and $y$ .

$6 - y = 2$

$x = 3 - y$

$6 - y = 2$

$x = 3 - y$

$6 - y = 2$

$x = 3 - y$

$6 - y = 2$

$x = 3 - y$

Step 3

Solve for $y$ in $6 - y = 2$ .

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

Subtract $6$ from both sides of the equation.

$- y = 2 - 6$

$x = 3 - y$

Subtract $6$ from $2$ .

$- y = - 4$

$x = 3 - y$

$- y = - 4$

$x = 3 - y$

Divide each term in $- y = - 4$ by $- 1$ and simplify.

Divide each term in $- y = - 4$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 4}{- 1}$

$x = 3 - y$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 4}{- 1}$

$x = 3 - y$

Divide $y$ by $1$ .

$y = \frac{- 4}{- 1}$

$x = 3 - y$

$y = \frac{- 4}{- 1}$

$x = 3 - y$

Simplify the right side.

Divide $- 4$ by $- 1$ .

$y = 4$

$x = 3 - y$

$y = 4$

$x = 3 - y$

$y = 4$

$x = 3 - y$

$y = 4$

$x = 3 - y$

Step 4

Replace all occurrences of $y$ with $4$ in each equation.

Replace all occurrences of $y$ in $x = 3 - y$ with $4$ .

$x = 3 - (4)$

$y = 4$

Simplify the right side.

Simplify $3 - (4)$ .

Multiply $- 1$ by $4$ .

$x = 3 - 4$

$y = 4$

Subtract $4$ from $3$ .

$x = - 1$

$y = 4$

$x = - 1$

$y = 4$

$x = - 1$

$y = 4$

$x = - 1$

$y = 4$

Step 5

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

$(- 1, 4)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 1, 4)$

Equation Form:

$x = - 1, y = 4$

Step 7

Solve the System of Equations x+y=3 2x+y=2

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