Solve the System of @WORD x+2y=2 , x-y=0

$x + 2 y = 2$ , $x - y = 0$

Step 1

Subtract $2 y$ from both sides of the equation.

$x = 2 - 2 y$

$x - y = 0$

Step 2

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

Replace all occurrences of $x$ in $x - y = 0$ with $2 - 2 y$ .

$(2 - 2 y) - y = 0$

$x = 2 - 2 y$

Simplify the left side.

Subtract $y$ from $- 2 y$ .

$2 - 3 y = 0$

$x = 2 - 2 y$

$2 - 3 y = 0$

$x = 2 - 2 y$

$2 - 3 y = 0$

$x = 2 - 2 y$

Step 3

Solve for $y$ in $2 - 3 y = 0$ .

Subtract $2$ from both sides of the equation.

$- 3 y = - 2$

$x = 2 - 2 y$

Divide each term in $- 3 y = - 2$ by $- 3$ and simplify.

Divide each term in $- 3 y = - 2$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 2}{- 3}$

$x = 2 - 2 y$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 2}{- 3}$

$x = 2 - 2 y$

Divide $y$ by $1$ .

$y = \frac{- 2}{- 3}$

$x = 2 - 2 y$

$y = \frac{- 2}{- 3}$

$x = 2 - 2 y$

$y = \frac{- 2}{- 3}$

$x = 2 - 2 y$

Simplify the right side.

Dividing two negative values results in a positive value.

$y = \frac{2}{3}$

$x = 2 - 2 y$

$y = \frac{2}{3}$

$x = 2 - 2 y$

$y = \frac{2}{3}$

$x = 2 - 2 y$

$y = \frac{2}{3}$

$x = 2 - 2 y$

Step 4

Replace all occurrences of $y$ with $\frac{2}{3}$ in each equation.

Replace all occurrences of $y$ in $x = 2 - 2 y$ with $\frac{2}{3}$ .

$x = 2 - 2 (\frac{2}{3})$

$y = \frac{2}{3}$

Simplify the right side.

Simplify $2 - 2 (\frac{2}{3})$ .

Simplify each term.

Multiply $- 2 (\frac{2}{3})$ .

Combine $- 2$ and $\frac{2}{3}$ .

$x = 2 + \frac{- 2 \cdot 2}{3}$

$y = \frac{2}{3}$

Multiply $- 2$ by $2$ .

$x = 2 + \frac{- 4}{3}$

$y = \frac{2}{3}$

$x = 2 + \frac{- 4}{3}$

$y = \frac{2}{3}$

Move the negative in front of the fraction.

$x = 2 - \frac{4}{3}$

$y = \frac{2}{3}$

$x = 2 - \frac{4}{3}$

$y = \frac{2}{3}$

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = 2 \cdot \frac{3}{3} - \frac{4}{3}$

$y = \frac{2}{3}$

Combine $2$ and $\frac{3}{3}$ .

$x = \frac{2 \cdot 3}{3} - \frac{4}{3}$

$y = \frac{2}{3}$

Combine the numerators over the common denominator.

$x = \frac{2 \cdot 3 - 4}{3}$

$y = \frac{2}{3}$

Simplify the numerator.

Multiply $2$ by $3$ .

$x = \frac{6 - 4}{3}$

$y = \frac{2}{3}$

Subtract $4$ from $6$ .

$x = \frac{2}{3}$

$y = \frac{2}{3}$

$x = \frac{2}{3}$

$y = \frac{2}{3}$

$x = \frac{2}{3}$

$y = \frac{2}{3}$

$x = \frac{2}{3}$

$y = \frac{2}{3}$

$x = \frac{2}{3}$

$y = \frac{2}{3}$

Step 5

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

$(\frac{2}{3}, \frac{2}{3})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(\frac{2}{3}, \frac{2}{3})$

Equation Form:

$x = \frac{2}{3}, y = \frac{2}{3}$

Step 7

Solve the System of @WORD x+2y=2 , x-y=0

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