Solve the System of Equations -2x+y=0 -7x+3y=2

$- 2 x + y = 0$ $- 7 x + 3 y = 2$

Add $2 x$ to both sides of the equation.

$y = 2 x$

$- 7 x + 3 y = 2$

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

Replace all occurrences of $y$ in $- 7 x + 3 y = 2$ with $2 x$ .

$- 7 x + 3 (2 x) = 2$

$y = 2 x$

Simplify the left side.

Simplify $- 7 x + 3 (2 x)$ .

Multiply $2$ by $3$ .

$- 7 x + 6 x = 2$

$y = 2 x$

Add $- 7 x$ and $6 x$ .

$- x = 2$

$y = 2 x$

$- x = 2$

$y = 2 x$

$- x = 2$

$y = 2 x$

$- x = 2$

$y = 2 x$

Divide each term in $- x = 2$ by $- 1$ and simplify.

Divide each term in $- x = 2$ by $- 1$ .

$\frac{- x}{- 1} = \frac{2}{- 1}$

$y = 2 x$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{2}{- 1}$

$y = 2 x$

Divide $x$ by $1$ .

$x = \frac{2}{- 1}$

$y = 2 x$

$x = \frac{2}{- 1}$

$y = 2 x$

Simplify the right side.

Divide $2$ by $- 1$ .

$x = - 2$

$y = 2 x$

$x = - 2$

$y = 2 x$

$x = - 2$

$y = 2 x$

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

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

$y = 2 (- 2)$

$x = - 2$

Simplify the right side.

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:

$x = - 2, y = - 4$

Solve the System of Equations -2x+y=0 -7x+3y=2

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