Solve by Graphing -0.1x-0.3y=1.2 0.2x-0.5y=2

$- 0.1 x - 0.3 y = 1.2$ $0.2 x - 0.5 y = 2$

Step 1

Add $0.1 x$ to both sides of the equation.

$- 0.3 y = 1.2 + 0.1 x$

$0.2 x - 0.5 y = 2$

Step 2

Divide each term in $- 0.3 y = 1.2 + 0.1 x$ by $- 0.3$ and simplify.

Divide each term in $- 0.3 y = 1.2 + 0.1 x$ by $- 0.3$ .

$\frac{- 0.3 y}{- 0.3} = \frac{1.2}{- 0.3} + \frac{0.1 x}{- 0.3}$

$0.2 x - 0.5 y = 2$

Simplify the left side.

Cancel the common factor of $- 0.3$ .

Cancel the common factor.

$\frac{- 0.3 y}{- 0.3} = \frac{1.2}{- 0.3} + \frac{0.1 x}{- 0.3}$

$0.2 x - 0.5 y = 2$

Divide $y$ by $1$ .

$y = \frac{1.2}{- 0.3} + \frac{0.1 x}{- 0.3}$

$0.2 x - 0.5 y = 2$

$y = \frac{1.2}{- 0.3} + \frac{0.1 x}{- 0.3}$

$0.2 x - 0.5 y = 2$

$y = \frac{1.2}{- 0.3} + \frac{0.1 x}{- 0.3}$

$0.2 x - 0.5 y = 2$

Simplify the right side.

Simplify each term.

Divide $1.2$ by $- 0.3$ .

$y = - 4 + \frac{0.1 x}{- 0.3}$

$0.2 x - 0.5 y = 2$

Move the negative in front of the fraction.

$y = - 4 - \frac{0.1 x}{0.3}$

$0.2 x - 0.5 y = 2$

Factor $0.1$ out of $0.1 x$ .

$y = - 4 - \frac{0.1 (x)}{0.3}$

$0.2 x - 0.5 y = 2$

Factor $0.3$ out of $0.3$ .

$y = - 4 - \frac{0.1 (x)}{0.3 (1)}$

$0.2 x - 0.5 y = 2$

Separate fractions.

$y = - 4 - (\frac{0.1}{0.3} \cdot \frac{x}{1})$

$0.2 x - 0.5 y = 2$

Divide $0.1$ by $0.3$ .

$y = - 4 - (0.\overline{3} (\frac{x}{1}))$

$0.2 x - 0.5 y = 2$

Divide $x$ by $1$ .

$y = - 4 - (0.\overline{3} x)$

$0.2 x - 0.5 y = 2$

Multiply $0.\overline{3}$ by $- 1$ .

$y = - 4 - 0.\overline{3} x$

$0.2 x - 0.5 y = 2$

$y = - 4 - 0.\overline{3} x$

$0.2 x - 0.5 y = 2$

$y = - 4 - 0.\overline{3} x$

$0.2 x - 0.5 y = 2$

$y = - 4 - 0.\overline{3} x$

$0.2 x - 0.5 y = 2$

Step 3

Subtract $0.2 x$ from both sides of the equation.

$- 0.5 y = 2 - 0.2 x$

$y = - 4 - 0.\overline{3} x$

Step 4

Divide each term in $- 0.5 y = 2 - 0.2 x$ by $- 0.5$ and simplify.

Divide each term in $- 0.5 y = 2 - 0.2 x$ by $- 0.5$ .

$\frac{- 0.5 y}{- 0.5} = \frac{2}{- 0.5} + \frac{- 0.2 x}{- 0.5}$

$y = - 4 - 0.\overline{3} x$

Simplify the left side.

Cancel the common factor of $- 0.5$ .

Cancel the common factor.

$\frac{- 0.5 y}{- 0.5} = \frac{2}{- 0.5} + \frac{- 0.2 x}{- 0.5}$

$y = - 4 - 0.\overline{3} x$

Divide $y$ by $1$ .

$y = \frac{2}{- 0.5} + \frac{- 0.2 x}{- 0.5}$

$y = - 4 - 0.\overline{3} x$

$y = \frac{2}{- 0.5} + \frac{- 0.2 x}{- 0.5}$

$y = - 4 - 0.\overline{3} x$

$y = \frac{2}{- 0.5} + \frac{- 0.2 x}{- 0.5}$

$y = - 4 - 0.\overline{3} x$

Simplify the right side.

Simplify each term.

Divide $2$ by $- 0.5$ .

$y = - 4 + \frac{- 0.2 x}{- 0.5}$

$y = - 4 - 0.\overline{3} x$

Dividing two negative values results in a positive value.

$y = - 4 + \frac{(0.2) x}{0.5}$

$y = - 4 - 0.\overline{3} x$

Factor $0.2$ out of $0.2 x$ .

$y = - 4 + \frac{0.2 (x)}{0.5}$

$y = - 4 - 0.\overline{3} x$

Factor $0.5$ out of $0.5$ .

$y = - 4 + \frac{0.2 (x)}{0.5 (1)}$

$y = - 4 - 0.\overline{3} x$

Separate fractions.

$y = - 4 + \frac{0.2}{0.5} \cdot \frac{x}{1}$

$y = - 4 - 0.\overline{3} x$

Divide $0.2$ by $0.5$ .

$y = - 4 + 0.4 (\frac{x}{1})$

$y = - 4 - 0.\overline{3} x$

Divide $x$ by $1$ .

$y = - 4 + 0.4 x$

$y = - 4 - 0.\overline{3} x$

$y = - 4 + 0.4 x$

$y = - 4 - 0.\overline{3} x$

$y = - 4 + 0.4 x$

$y = - 4 - 0.\overline{3} x$

$y = - 4 + 0.4 x$

$y = - 4 - 0.\overline{3} x$

Step 5

Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.

$(0, - 4)$

Step 6

Solve by Graphing -0.1x-0.3y=1.2 0.2x-0.5y=2

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