Solve the System of Equations x-2y=0 y=2x-3

$x - 2 y = 0$ $y = 2 x - 3$

Replace all occurrences of $y$ with $2 x - 3$ in each equation.

Replace all occurrences of $y$ in $x - 2 y = 0$ with $2 x - 3$ .

$x - 2 (2 x - 3) = 0$

$y = 2 x - 3$

Simplify the left side.

Simplify $x - 2 (2 x - 3)$ .

Simplify each term.

Apply the distributive property.

$x - 2 (2 x) - 2 \cdot - 3 = 0$

$y = 2 x - 3$

Multiply $2$ by $- 2$ .

$x - 4 x - 2 \cdot - 3 = 0$

$y = 2 x - 3$

Multiply $- 2$ by $- 3$ .

$x - 4 x + 6 = 0$

$y = 2 x - 3$

$x - 4 x + 6 = 0$

$y = 2 x - 3$

Subtract $4 x$ from $x$ .

$- 3 x + 6 = 0$

$y = 2 x - 3$

$- 3 x + 6 = 0$

$y = 2 x - 3$

$- 3 x + 6 = 0$

$y = 2 x - 3$

$- 3 x + 6 = 0$

$y = 2 x - 3$

Solve for $x$ in $- 3 x + 6 = 0$ .

Subtract $6$ from both sides of the equation.

$- 3 x = - 6$

$y = 2 x - 3$

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

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

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

$y = 2 x - 3$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

$y = 2 x - 3$

Divide $x$ by $1$ .

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

$y = 2 x - 3$

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

$y = 2 x - 3$

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

$y = 2 x - 3$

Simplify the right side.

Divide $- 6$ by $- 3$ .

$x = 2$

$y = 2 x - 3$

$x = 2$

$y = 2 x - 3$

$x = 2$

$y = 2 x - 3$

$x = 2$

$y = 2 x - 3$

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

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

$y = 2 (2) - 3$

$x = 2$

Simplify the right side.

Simplify $2 (2) - 3$ .

Multiply $2$ by $2$ .

$y = 4 - 3$

$x = 2$

Subtract $3$ from $4$ .

$y = 1$

$x = 2$

$y = 1$

$x = 2$

$y = 1$

$x = 2$

$y = 1$

$x = 2$

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

$(2, 1)$

The result can be shown in multiple forms.

Point Form:

$(2, 1)$

Equation Form:

$x = 2, y = 1$

Solve the System of Equations x-2y=0 y=2x-3

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