Solve the System of Equations 8-0.9x=0.4y -y+0.3x=1.6

$8 - 0.9 x = 0.4 y$ $- y + 0.3 x = 1.6$

Solve for $x$ in $8 - 0.9 x = 0.4 y$ .

Subtract $8$ from both sides of the equation.

$- 0.9 x = 0.4 y - 8$

$- y + 0.3 x = 1.6$

Divide each term in $- 0.9 x = 0.4 y - 8$ by $- 0.9$ and simplify.

Divide each term in $- 0.9 x = 0.4 y - 8$ by $- 0.9$ .

$\frac{- 0.9 x}{- 0.9} = \frac{0.4 y}{- 0.9} + \frac{- 8}{- 0.9}$

$- y + 0.3 x = 1.6$

Simplify the left side.

Cancel the common factor of $- 0.9$ .

Cancel the common factor.

$\frac{- 0.9 x}{- 0.9} = \frac{0.4 y}{- 0.9} + \frac{- 8}{- 0.9}$

$- y + 0.3 x = 1.6$

Divide $x$ by $1$ .

$x = \frac{0.4 y}{- 0.9} + \frac{- 8}{- 0.9}$

$- y + 0.3 x = 1.6$

$x = \frac{0.4 y}{- 0.9} + \frac{- 8}{- 0.9}$

$- y + 0.3 x = 1.6$

$x = \frac{0.4 y}{- 0.9} + \frac{- 8}{- 0.9}$

$- y + 0.3 x = 1.6$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{0.4 y}{0.9} + \frac{- 8}{- 0.9}$

$- y + 0.3 x = 1.6$

Factor $0.4$ out of $0.4 y$ .

$x = - \frac{0.4 (y)}{0.9} + \frac{- 8}{- 0.9}$

$- y + 0.3 x = 1.6$

Factor $0.9$ out of $0.9$ .

$x = - \frac{0.4 (y)}{0.9 (1)} + \frac{- 8}{- 0.9}$

$- y + 0.3 x = 1.6$

Separate fractions.

$x = - (\frac{0.4}{0.9} \cdot \frac{y}{1}) + \frac{- 8}{- 0.9}$

$- y + 0.3 x = 1.6$

Divide $0.4$ by $0.9$ .

$x = - (0.\overline{4} (\frac{y}{1})) + \frac{- 8}{- 0.9}$

$- y + 0.3 x = 1.6$

Divide $y$ by $1$ .

$x = - (0.\overline{4} y) + \frac{- 8}{- 0.9}$

$- y + 0.3 x = 1.6$

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

$x = - 0.\overline{4} y + \frac{- 8}{- 0.9}$

$- y + 0.3 x = 1.6$

Divide $- 8$ by $- 0.9$ .

$x = - 0.\overline{4} y + 8.\overline{8}$

$- y + 0.3 x = 1.6$

$x = - 0.\overline{4} y + 8.\overline{8}$

$- y + 0.3 x = 1.6$

$x = - 0.\overline{4} y + 8.\overline{8}$

$- y + 0.3 x = 1.6$

$x = - 0.\overline{4} y + 8.\overline{8}$

$- y + 0.3 x = 1.6$

$x = - 0.\overline{4} y + 8.\overline{8}$

$- y + 0.3 x = 1.6$

Replace all occurrences of $x$ with $- 0.\overline{4} y + 8.\overline{8}$ in each equation.

Replace all occurrences of $x$ in $- y + 0.3 x = 1.6$ with $- 0.\overline{4} y + 8.\overline{8}$ .

$- y + 0.3 (- 0.\overline{4} y + 8.\overline{8}) = 1.6$

$x = - 0.\overline{4} y + 8.\overline{8}$

Simplify the left side.

Simplify $- y + 0.3 (- 0.\overline{4} y + 8.\overline{8})$ .

Simplify each term.

Apply the distributive property.

$- y + 0.3 (- 0.\overline{4} y) + 0.3 \cdot 8.\overline{8} = 1.6$

$x = - 0.\overline{4} y + 8.\overline{8}$

Multiply $- 0.\overline{4}$ by $0.3$ .

$- y - 0.1\overline{3} y + 0.3 \cdot 8.\overline{8} = 1.6$

$x = - 0.\overline{4} y + 8.\overline{8}$

Multiply $0.3$ by $8.\overline{8}$ .

$- y - 0.1\overline{3} y + 2.\overline{6} = 1.6$

$x = - 0.\overline{4} y + 8.\overline{8}$

$- y - 0.1\overline{3} y + 2.\overline{6} = 1.6$

$x = - 0.\overline{4} y + 8.\overline{8}$

Subtract $0.1\overline{3} y$ from $- y$ .

$- 1.1\overline{3} y + 2.\overline{6} = 1.6$

$x = - 0.\overline{4} y + 8.\overline{8}$

$- 1.1\overline{3} y + 2.\overline{6} = 1.6$

$x = - 0.\overline{4} y + 8.\overline{8}$

$- 1.1\overline{3} y + 2.\overline{6} = 1.6$

$x = - 0.\overline{4} y + 8.\overline{8}$

$- 1.1\overline{3} y + 2.\overline{6} = 1.6$

$x = - 0.\overline{4} y + 8.\overline{8}$

Solve for $y$ in $- 1.1\overline{3} y + 2.\overline{6} = 1.6$ .

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

Subtract $2.\overline{6}$ from both sides of the equation.

$- 1.1\overline{3} y = 1.6 - 2.\overline{6}$

$x = - 0.\overline{4} y + 8.\overline{8}$

Subtract $2.\overline{6}$ from $1.6$ .

$- 1.1\overline{3} y = - 1.0\overline{6}$

$x = - 0.\overline{4} y + 8.\overline{8}$

$- 1.1\overline{3} y = - 1.0\overline{6}$

$x = - 0.\overline{4} y + 8.\overline{8}$

Divide each term in $- 1.1\overline{3} y = - 1.0\overline{6}$ by $- 1.1\overline{3}$ and simplify.

Divide each term in $- 1.1\overline{3} y = - 1.0\overline{6}$ by $- 1.1\overline{3}$ .

$\frac{- 1.1\overline{3} y}{- 1.1\overline{3}} = \frac{- 1.0\overline{6}}{- 1.1\overline{3}}$

$x = - 0.\overline{4} y + 8.\overline{8}$

Simplify the left side.

Cancel the common factor of $- 1.1\overline{3}$ .

Cancel the common factor.

$\frac{- 1.1\overline{3} y}{- 1.1\overline{3}} = \frac{- 1.0\overline{6}}{- 1.1\overline{3}}$

$x = - 0.\overline{4} y + 8.\overline{8}$

Divide $y$ by $1$ .

$y = \frac{- 1.0\overline{6}}{- 1.1\overline{3}}$

$x = - 0.\overline{4} y + 8.\overline{8}$

$y = \frac{- 1.0\overline{6}}{- 1.1\overline{3}}$

$x = - 0.\overline{4} y + 8.\overline{8}$

$y = \frac{- 1.0\overline{6}}{- 1.1\overline{3}}$

$x = - 0.\overline{4} y + 8.\overline{8}$

Simplify the right side.

Divide $- 1.0\overline{6}$ by $- 1.1\overline{3}$ .

$y = 0.94117647$

$x = - 0.\overline{4} y + 8.\overline{8}$

$y = 0.94117647$

$x = - 0.\overline{4} y + 8.\overline{8}$

$y = 0.94117647$

$x = - 0.\overline{4} y + 8.\overline{8}$

$y = 0.94117647$

$x = - 0.\overline{4} y + 8.\overline{8}$

Replace all occurrences of $y$ with $0.94117647$ in each equation.

Replace all occurrences of $y$ in $x = - 0.\overline{4} y + 8.\overline{8}$ with $0.94117647$ .

$x = - 0.\overline{4} \cdot 0.94117647 + 8.\overline{8}$

$y = 0.94117647$

Simplify the right side.

Simplify $- 0.\overline{4} \cdot 0.94117647 + 8.\overline{8}$ .

Multiply $- 0.\overline{4}$ by $0.94117647$ .

$x = - 0.41830065 + 8.\overline{8}$

$y = 0.94117647$

Add $- 0.41830065$ and $8.\overline{8}$ .

$x = 8.47058823$

$y = 0.94117647$

$x = 8.47058823$

$y = 0.94117647$

$x = 8.47058823$

$y = 0.94117647$

$x = 8.47058823$

$y = 0.94117647$

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

$(8.47058823, 0.94117647)$

The result can be shown in multiple forms.

Point Form:

$(8.47058823, 0.94117647)$

Equation Form:

$x = 8.47058823, y = 0.94117647$

Related Questions