Solve the System of Equations 6-0.9x=0.4y -y+0.2x=3.6

$6 - 0.9 x = 0.4 y$ $- y + 0.2 x = 3.6$

Solve for $x$ in $6 - 0.9 x = 0.4 y$ .

Subtract $6$ from both sides of the equation.

$- 0.9 x = 0.4 y - 6$

$- y + 0.2 x = 3.6$

Divide each term in $- 0.9 x = 0.4 y - 6$ by $- 0.9$ and simplify.

Divide each term in $- 0.9 x = 0.4 y - 6$ by $- 0.9$ .

$\frac{- 0.9 x}{- 0.9} = \frac{0.4 y}{- 0.9} + \frac{- 6}{- 0.9}$

$- y + 0.2 x = 3.6$

Simplify the left side.

Cancel the common factor of $- 0.9$ .

Cancel the common factor.

$\frac{- 0.9 x}{- 0.9} = \frac{0.4 y}{- 0.9} + \frac{- 6}{- 0.9}$

$- y + 0.2 x = 3.6$

Divide $x$ by $1$ .

$x = \frac{0.4 y}{- 0.9} + \frac{- 6}{- 0.9}$

$- y + 0.2 x = 3.6$

$x = \frac{0.4 y}{- 0.9} + \frac{- 6}{- 0.9}$

$- y + 0.2 x = 3.6$

$x = \frac{0.4 y}{- 0.9} + \frac{- 6}{- 0.9}$

$- y + 0.2 x = 3.6$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{0.4 y}{0.9} + \frac{- 6}{- 0.9}$

$- y + 0.2 x = 3.6$

Factor $0.4$ out of $0.4 y$ .

$x = - \frac{0.4 (y)}{0.9} + \frac{- 6}{- 0.9}$

$- y + 0.2 x = 3.6$

Factor $0.9$ out of $0.9$ .

$x = - \frac{0.4 (y)}{0.9 (1)} + \frac{- 6}{- 0.9}$

$- y + 0.2 x = 3.6$

Separate fractions.

$x = - (\frac{0.4}{0.9} \cdot \frac{y}{1}) + \frac{- 6}{- 0.9}$

$- y + 0.2 x = 3.6$

Divide $0.4$ by $0.9$ .

$x = - (0.\overline{4} (\frac{y}{1})) + \frac{- 6}{- 0.9}$

$- y + 0.2 x = 3.6$

Divide $y$ by $1$ .

$x = - (0.\overline{4} y) + \frac{- 6}{- 0.9}$

$- y + 0.2 x = 3.6$

Multiply $0.\overline{4}$ by $- 1$ .

$x = - 0.\overline{4} y + \frac{- 6}{- 0.9}$

$- y + 0.2 x = 3.6$

Divide $- 6$ by $- 0.9$ .

$x = - 0.\overline{4} y + 6.\overline{6}$

$- y + 0.2 x = 3.6$

$x = - 0.\overline{4} y + 6.\overline{6}$

$- y + 0.2 x = 3.6$

$x = - 0.\overline{4} y + 6.\overline{6}$

$- y + 0.2 x = 3.6$

$x = - 0.\overline{4} y + 6.\overline{6}$

$- y + 0.2 x = 3.6$

$x = - 0.\overline{4} y + 6.\overline{6}$

$- y + 0.2 x = 3.6$

Replace all occurrences of $x$ with $- 0.\overline{4} y + 6.\overline{6}$ in each equation.

Replace all occurrences of $x$ in $- y + 0.2 x = 3.6$ with $- 0.\overline{4} y + 6.\overline{6}$ .

$- y + 0.2 (- 0.\overline{4} y + 6.\overline{6}) = 3.6$

$x = - 0.\overline{4} y + 6.\overline{6}$

Simplify the left side.

Simplify $- y + 0.2 (- 0.\overline{4} y + 6.\overline{6})$ .

Simplify each term.

Apply the distributive property.

$- y + 0.2 (- 0.\overline{4} y) + 0.2 \cdot 6.\overline{6} = 3.6$

$x = - 0.\overline{4} y + 6.\overline{6}$

Multiply $- 0.\overline{4}$ by $0.2$ .

$- y - 0.0\overline{8} y + 0.2 \cdot 6.\overline{6} = 3.6$

$x = - 0.\overline{4} y + 6.\overline{6}$

Multiply $0.2$ by $6.\overline{6}$ .

$- y - 0.0\overline{8} y + 1.\overline{3} = 3.6$

$x = - 0.\overline{4} y + 6.\overline{6}$

$- y - 0.0\overline{8} y + 1.\overline{3} = 3.6$

$x = - 0.\overline{4} y + 6.\overline{6}$

Subtract $0.0\overline{8} y$ from $- y$ .

$- 1.0\overline{8} y + 1.\overline{3} = 3.6$

$x = - 0.\overline{4} y + 6.\overline{6}$

$- 1.0\overline{8} y + 1.\overline{3} = 3.6$

$x = - 0.\overline{4} y + 6.\overline{6}$

$- 1.0\overline{8} y + 1.\overline{3} = 3.6$

$x = - 0.\overline{4} y + 6.\overline{6}$

$- 1.0\overline{8} y + 1.\overline{3} = 3.6$

$x = - 0.\overline{4} y + 6.\overline{6}$

Solve for $y$ in $- 1.0\overline{8} y + 1.\overline{3} = 3.6$ .

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

Subtract $1.\overline{3}$ from both sides of the equation.

$- 1.0\overline{8} y = 3.6 - 1.\overline{3}$

$x = - 0.\overline{4} y + 6.\overline{6}$

Subtract $1.\overline{3}$ from $3.6$ .

$- 1.0\overline{8} y = 2.2\overline{6}$

$x = - 0.\overline{4} y + 6.\overline{6}$

$- 1.0\overline{8} y = 2.2\overline{6}$

$x = - 0.\overline{4} y + 6.\overline{6}$

Divide each term in $- 1.0\overline{8} y = 2.2\overline{6}$ by $- 1.0\overline{8}$ and simplify.

Divide each term in $- 1.0\overline{8} y = 2.2\overline{6}$ by $- 1.0\overline{8}$ .

$\frac{- 1.0\overline{8} y}{- 1.0\overline{8}} = \frac{2.2\overline{6}}{- 1.0\overline{8}}$

$x = - 0.\overline{4} y + 6.\overline{6}$

Simplify the left side.

Cancel the common factor of $- 1.0\overline{8}$ .

Cancel the common factor.

$\frac{- 1.0\overline{8} y}{- 1.0\overline{8}} = \frac{2.2\overline{6}}{- 1.0\overline{8}}$

$x = - 0.\overline{4} y + 6.\overline{6}$

Divide $y$ by $1$ .

$y = \frac{2.2\overline{6}}{- 1.0\overline{8}}$

$x = - 0.\overline{4} y + 6.\overline{6}$

$y = \frac{2.2\overline{6}}{- 1.0\overline{8}}$

$x = - 0.\overline{4} y + 6.\overline{6}$

$y = \frac{2.2\overline{6}}{- 1.0\overline{8}}$

$x = - 0.\overline{4} y + 6.\overline{6}$

Simplify the right side.

Divide $2.2\overline{6}$ by $- 1.0\overline{8}$ .

$y = - 2.08163265$

$x = - 0.\overline{4} y + 6.\overline{6}$

$y = - 2.08163265$

$x = - 0.\overline{4} y + 6.\overline{6}$

$y = - 2.08163265$

$x = - 0.\overline{4} y + 6.\overline{6}$

$y = - 2.08163265$

$x = - 0.\overline{4} y + 6.\overline{6}$

Replace all occurrences of $y$ with $- 2.08163265$ in each equation.

Replace all occurrences of $y$ in $x = - 0.\overline{4} y + 6.\overline{6}$ with $- 2.08163265$ .

$x = - 0.\overline{4} \cdot - 2.08163265 + 6.\overline{6}$

$y = - 2.08163265$

Simplify the right side.

Simplify $- 0.\overline{4} \cdot - 2.08163265 + 6.\overline{6}$ .

Multiply $- 0.\overline{4}$ by $- 2.08163265$ .

$x = 0.92517006 + 6.\overline{6}$

$y = - 2.08163265$

Add $0.92517006$ and $6.\overline{6}$ .

$x = 7.59183673$

$y = - 2.08163265$

$x = 7.59183673$

$y = - 2.08163265$

$x = 7.59183673$

$y = - 2.08163265$

$x = 7.59183673$

$y = - 2.08163265$

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

$(7.59183673, - 2.08163265)$

The result can be shown in multiple forms.

Point Form:

$(7.59183673, - 2.08163265)$

Equation Form:

$x = 7.59183673, y = - 2.08163265$

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