Solve the System of Equations x-2y=6 y=2x

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Algebra

$x - 2 y = 6$ $y = 2 x$

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

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Replace all occurrences of $y$ in $x - 2 y = 6$ with $2 x$ .

$x - 2 (2 x) = 6$

$y = 2 x$

Simplify the left side.

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Simplify $x - 2 (2 x)$ .

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Multiply $2$ by $- 2$ .

$x - 4 x = 6$

$y = 2 x$

Subtract $4 x$ from $x$ .

$- 3 x = 6$

$y = 2 x$

$- 3 x = 6$

$y = 2 x$

$- 3 x = 6$

$y = 2 x$

$- 3 x = 6$

$y = 2 x$

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

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

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

$y = 2 x$

Simplify the left side.

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Cancel the common factor of $- 3$ .

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Cancel the common factor.

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

$y = 2 x$

Divide $x$ by $1$ .

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

$y = 2 x$

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

$y = 2 x$

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

$y = 2 x$

Simplify the right side.

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Divide $6$ by $- 3$ .

$x = - 2$

$y = 2 x$

$x = - 2$

$y = 2 x$

$x = - 2$

$y = 2 x$

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

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

$y = 2 (- 2)$

$x = - 2$

Simplify the right side.

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Multiply $2$ by $- 2$ .

$y = - 4$

$x = - 2$

$y = - 4$

$x = - 2$

$y = - 4$

$x = - 2$

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

$(- 2, - 4)$

The result can be shown in multiple forms.

Point Form:

$(- 2, - 4)$

Equation Form:

$x = - 2, y = - 4$

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