Solve the System of Equations 0.6x-y=1.03 3-0.3x=0.1y

$0.6 x - y = 1.03$ $3 - 0.3 x = 0.1 y$

Step 1

Solve for $x$ in $0.6 x - y = 1.03$ .

Add $y$ to both sides of the equation.

$0.6 x = 1.03 + y$

$3 - 0.3 x = 0.1 y$

Divide each term in $0.6 x = 1.03 + y$ by $0.6$ and simplify.

Divide each term in $0.6 x = 1.03 + y$ by $0.6$ .

$\frac{0.6 x}{0.6} = \frac{1.03}{0.6} + \frac{y}{0.6}$

$3 - 0.3 x = 0.1 y$

Simplify the left side.

Cancel the common factor of $0.6$ .

Cancel the common factor.

$\frac{0.6 x}{0.6} = \frac{1.03}{0.6} + \frac{y}{0.6}$

$3 - 0.3 x = 0.1 y$

Divide $x$ by $1$ .

$x = \frac{1.03}{0.6} + \frac{y}{0.6}$

$3 - 0.3 x = 0.1 y$

$x = \frac{1.03}{0.6} + \frac{y}{0.6}$

$3 - 0.3 x = 0.1 y$

$x = \frac{1.03}{0.6} + \frac{y}{0.6}$

$3 - 0.3 x = 0.1 y$

Simplify the right side.

Simplify each term.

Divide $1.03$ by $0.6$ .

$x = 1.71\overline{6} + \frac{y}{0.6}$

$3 - 0.3 x = 0.1 y$

Multiply by $1$ .

$x = 1.71\overline{6} + \frac{1 y}{0.6}$

$3 - 0.3 x = 0.1 y$

Factor $0.6$ out of $0.6$ .

$x = 1.71\overline{6} + \frac{1 y}{0.6 (1)}$

$3 - 0.3 x = 0.1 y$

Separate fractions.

$x = 1.71\overline{6} + \frac{1}{0.6} \cdot \frac{y}{1}$

$3 - 0.3 x = 0.1 y$

Divide $1$ by $0.6$ .

$x = 1.71\overline{6} + 1.\overline{6} (\frac{y}{1})$

$3 - 0.3 x = 0.1 y$

Divide $y$ by $1$ .

$x = 1.71\overline{6} + 1.\overline{6} y$

$3 - 0.3 x = 0.1 y$

$x = 1.71\overline{6} + 1.\overline{6} y$

$3 - 0.3 x = 0.1 y$

$x = 1.71\overline{6} + 1.\overline{6} y$

$3 - 0.3 x = 0.1 y$

$x = 1.71\overline{6} + 1.\overline{6} y$

$3 - 0.3 x = 0.1 y$

$x = 1.71\overline{6} + 1.\overline{6} y$

$3 - 0.3 x = 0.1 y$

Step 2

Replace all occurrences of $x$ with $1.71\overline{6} + 1.\overline{6} y$ in each equation.

Replace all occurrences of $x$ in $3 - 0.3 x = 0.1 y$ with $1.71\overline{6} + 1.\overline{6} y$ .

$3 - 0.3 (1.71\overline{6} + 1.\overline{6} y) = 0.1 y$

$x = 1.71\overline{6} + 1.\overline{6} y$

Simplify the left side.

Simplify $3 - 0.3 (1.71\overline{6} + 1.\overline{6} y)$ .

Simplify each term.

Apply the distributive property.

$3 - 0.3 \cdot 1.71\overline{6} - 0.3 (1.\overline{6} y) = 0.1 y$

$x = 1.71\overline{6} + 1.\overline{6} y$

Multiply $- 0.3$ by $1.71\overline{6}$ .

$3 - 0.515 - 0.3 (1.\overline{6} y) = 0.1 y$

$x = 1.71\overline{6} + 1.\overline{6} y$

Multiply $1.\overline{6}$ by $- 0.3$ .

$3 - 0.515 - 0.5 y = 0.1 y$

$x = 1.71\overline{6} + 1.\overline{6} y$

$3 - 0.515 - 0.5 y = 0.1 y$

$x = 1.71\overline{6} + 1.\overline{6} y$

Subtract $0.515$ from $3$ .

$2.485 - 0.5 y = 0.1 y$

$x = 1.71\overline{6} + 1.\overline{6} y$

$2.485 - 0.5 y = 0.1 y$

$x = 1.71\overline{6} + 1.\overline{6} y$

$2.485 - 0.5 y = 0.1 y$

$x = 1.71\overline{6} + 1.\overline{6} y$

$2.485 - 0.5 y = 0.1 y$

$x = 1.71\overline{6} + 1.\overline{6} y$

Step 3

Solve for $y$ in $2.485 - 0.5 y = 0.1 y$ .

Move all terms containing $y$ to the left side of the equation.

Subtract $0.1 y$ from both sides of the equation.

$2.485 - 0.5 y - 0.1 y = 0$

$x = 1.71\overline{6} + 1.\overline{6} y$

Subtract $0.1 y$ from $- 0.5 y$ .

$2.485 - 0.6 y = 0$

$x = 1.71\overline{6} + 1.\overline{6} y$

$2.485 - 0.6 y = 0$

$x = 1.71\overline{6} + 1.\overline{6} y$

Subtract $2.485$ from both sides of the equation.

$- 0.6 y = - 2.485$

$x = 1.71\overline{6} + 1.\overline{6} y$

Divide each term in $- 0.6 y = - 2.485$ by $- 0.6$ and simplify.

Divide each term in $- 0.6 y = - 2.485$ by $- 0.6$ .

$\frac{- 0.6 y}{- 0.6} = \frac{- 2.485}{- 0.6}$

$x = 1.71\overline{6} + 1.\overline{6} y$

Simplify the left side.

Cancel the common factor of $- 0.6$ .

Cancel the common factor.

$\frac{- 0.6 y}{- 0.6} = \frac{- 2.485}{- 0.6}$

$x = 1.71\overline{6} + 1.\overline{6} y$

Divide $y$ by $1$ .

$y = \frac{- 2.485}{- 0.6}$

$x = 1.71\overline{6} + 1.\overline{6} y$

$y = \frac{- 2.485}{- 0.6}$

$x = 1.71\overline{6} + 1.\overline{6} y$

$y = \frac{- 2.485}{- 0.6}$

$x = 1.71\overline{6} + 1.\overline{6} y$

Simplify the right side.

Divide $- 2.485$ by $- 0.6$ .

$y = 4.141\overline{6}$

$x = 1.71\overline{6} + 1.\overline{6} y$

$y = 4.141\overline{6}$

$x = 1.71\overline{6} + 1.\overline{6} y$

$y = 4.141\overline{6}$

$x = 1.71\overline{6} + 1.\overline{6} y$

$y = 4.141\overline{6}$

$x = 1.71\overline{6} + 1.\overline{6} y$

Step 4

Replace all occurrences of $y$ with $4.141\overline{6}$ in each equation.

Replace all occurrences of $y$ in $x = 1.71\overline{6} + 1.\overline{6} y$ with $4.141\overline{6}$ .

$x = 1.71\overline{6} + 1.\overline{6} (4.141\overline{6})$

$y = 4.141\overline{6}$

Simplify the right side.

Simplify $1.71\overline{6} + 1.\overline{6} (4.141\overline{6})$ .

Multiply $1.\overline{6}$ by $4.141\overline{6}$ .

$x = 1.71\overline{6} + 6.902\overline{7}$

$y = 4.141\overline{6}$

Add $1.71\overline{6}$ and $6.902\overline{7}$ .

$x = 8.619\overline{4}$

$y = 4.141\overline{6}$

$x = 8.619\overline{4}$

$y = 4.141\overline{6}$

$x = 8.619\overline{4}$

$y = 4.141\overline{6}$

$x = 8.619\overline{4}$

$y = 4.141\overline{6}$

Step 5

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

$(8.619\overline{4}, 4.141\overline{6})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(8.619\overline{4}, 4.141\overline{6})$

Equation Form:

$x = 8.619\overline{4}, y = 4.141\overline{6}$

Step 7

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