Solve the System of Equations 0.7x-y=5.16 2-0.8x=0.4y

$0.7 x - y = 5.16$ $2 - 0.8 x = 0.4 y$

Step 1

Solve for $x$ in $0.7 x - y = 5.16$ .

Add $y$ to both sides of the equation.

$0.7 x = 5.16 + y$

$2 - 0.8 x = 0.4 y$

Divide each term in $0.7 x = 5.16 + y$ by $0.7$ and simplify.

Divide each term in $0.7 x = 5.16 + y$ by $0.7$ .

$\frac{0.7 x}{0.7} = \frac{5.16}{0.7} + \frac{y}{0.7}$

$2 - 0.8 x = 0.4 y$

Simplify the left side.

Cancel the common factor of $0.7$ .

Cancel the common factor.

$\frac{0.7 x}{0.7} = \frac{5.16}{0.7} + \frac{y}{0.7}$

$2 - 0.8 x = 0.4 y$

Divide $x$ by $1$ .

$x = \frac{5.16}{0.7} + \frac{y}{0.7}$

$2 - 0.8 x = 0.4 y$

$x = \frac{5.16}{0.7} + \frac{y}{0.7}$

$2 - 0.8 x = 0.4 y$

$x = \frac{5.16}{0.7} + \frac{y}{0.7}$

$2 - 0.8 x = 0.4 y$

Simplify the right side.

Simplify each term.

Divide $5.16$ by $0.7$ .

$x = 7.3\overline{714285} + \frac{y}{0.7}$

$2 - 0.8 x = 0.4 y$

Multiply by $1$ .

$x = 7.3\overline{714285} + \frac{1 y}{0.7}$

$2 - 0.8 x = 0.4 y$

Factor $0.7$ out of $0.7$ .

$x = 7.3\overline{714285} + \frac{1 y}{0.7 (1)}$

$2 - 0.8 x = 0.4 y$

Separate fractions.

$x = 7.3\overline{714285} + \frac{1}{0.7} \cdot \frac{y}{1}$

$2 - 0.8 x = 0.4 y$

Divide $1$ by $0.7$ .

$x = 7.3\overline{714285} + 1.\overline{428571} (\frac{y}{1})$

$2 - 0.8 x = 0.4 y$

Divide $y$ by $1$ .

$x = 7.3\overline{714285} + 1.\overline{428571} y$

$2 - 0.8 x = 0.4 y$

$x = 7.3\overline{714285} + 1.\overline{428571} y$

$2 - 0.8 x = 0.4 y$

$x = 7.3\overline{714285} + 1.\overline{428571} y$

$2 - 0.8 x = 0.4 y$

$x = 7.3\overline{714285} + 1.\overline{428571} y$

$2 - 0.8 x = 0.4 y$

$x = 7.3\overline{714285} + 1.\overline{428571} y$

$2 - 0.8 x = 0.4 y$

Step 2

Replace all occurrences of $x$ with $7.3\overline{714285} + 1.\overline{428571} y$ in each equation.

Replace all occurrences of $x$ in $2 - 0.8 x = 0.4 y$ with $7.3\overline{714285} + 1.\overline{428571} y$ .

$2 - 0.8 (7.3\overline{714285} + 1.\overline{428571} y) = 0.4 y$

$x = 7.3\overline{714285} + 1.\overline{428571} y$

Simplify the left side.

Simplify $2 - 0.8 (7.3\overline{714285} + 1.\overline{428571} y)$ .

Simplify each term.

Apply the distributive property.

$2 - 0.8 \cdot 7.3\overline{714285} - 0.8 (1.\overline{428571} y) = 0.4 y$

$x = 7.3\overline{714285} + 1.\overline{428571} y$

Multiply $- 0.8$ by $7.3\overline{714285}$ .

$2 - 5.89714285 - 0.8 (1.\overline{428571} y) = 0.4 y$

$x = 7.3\overline{714285} + 1.\overline{428571} y$

Multiply $1.\overline{428571}$ by $- 0.8$ .

$2 - 5.89714285 - 1.\overline{142857} y = 0.4 y$

$x = 7.3\overline{714285} + 1.\overline{428571} y$

$2 - 5.89714285 - 1.\overline{142857} y = 0.4 y$

$x = 7.3\overline{714285} + 1.\overline{428571} y$

Subtract $5.89714285$ from $2$ .

$- 3.89714285 - 1.\overline{142857} y = 0.4 y$

$x = 7.3\overline{714285} + 1.\overline{428571} y$

$- 3.89714285 - 1.\overline{142857} y = 0.4 y$

$x = 7.3\overline{714285} + 1.\overline{428571} y$

$- 3.89714285 - 1.\overline{142857} y = 0.4 y$

$x = 7.3\overline{714285} + 1.\overline{428571} y$

$- 3.89714285 - 1.\overline{142857} y = 0.4 y$

$x = 7.3\overline{714285} + 1.\overline{428571} y$

Step 3

Solve for $y$ in $- 3.89714285 - 1.\overline{142857} y = 0.4 y$ .

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

Subtract $0.4 y$ from both sides of the equation.

$- 3.89714285 - 1.\overline{142857} y - 0.4 y = 0$

$x = 7.3\overline{714285} + 1.\overline{428571} y$

Subtract $0.4 y$ from $- 1.\overline{142857} y$ .

$- 3.89714285 - 1.5\overline{428571} y = 0$

$x = 7.3\overline{714285} + 1.\overline{428571} y$

$- 3.89714285 - 1.5\overline{428571} y = 0$

$x = 7.3\overline{714285} + 1.\overline{428571} y$

Add $3.89714285$ to both sides of the equation.

$- 1.5\overline{428571} y = 3.89714285$

$x = 7.3\overline{714285} + 1.\overline{428571} y$

Divide each term in $- 1.5\overline{428571} y = 3.89714285$ by $- 1.5\overline{428571}$ and simplify.

Divide each term in $- 1.5\overline{428571} y = 3.89714285$ by $- 1.5\overline{428571}$ .

$\frac{- 1.5\overline{428571} y}{- 1.5\overline{428571}} = \frac{3.89714285}{- 1.5\overline{428571}}$

$x = 7.3\overline{714285} + 1.\overline{428571} y$

Simplify the left side.

Cancel the common factor of $- 1.5\overline{428571}$ .

Cancel the common factor.

$\frac{- 1.5\overline{428571} y}{- 1.5\overline{428571}} = \frac{3.89714285}{- 1.5\overline{428571}}$

$x = 7.3\overline{714285} + 1.\overline{428571} y$

Divide $y$ by $1$ .

$y = \frac{3.89714285}{- 1.5\overline{428571}}$

$x = 7.3\overline{714285} + 1.\overline{428571} y$

$y = \frac{3.89714285}{- 1.5\overline{428571}}$

$x = 7.3\overline{714285} + 1.\overline{428571} y$

$y = \frac{3.89714285}{- 1.5\overline{428571}}$

$x = 7.3\overline{714285} + 1.\overline{428571} y$

Simplify the right side.

Divide $3.89714285$ by $- 1.5\overline{428571}$ .

$y = - 2.5\overline{259}$

$x = 7.3\overline{714285} + 1.\overline{428571} y$

$y = - 2.5\overline{259}$

$x = 7.3\overline{714285} + 1.\overline{428571} y$

$y = - 2.5\overline{259}$

$x = 7.3\overline{714285} + 1.\overline{428571} y$

$y = - 2.5\overline{259}$

$x = 7.3\overline{714285} + 1.\overline{428571} y$

Step 4

Replace all occurrences of $y$ with $- 2.5\overline{259}$ in each equation.

Replace all occurrences of $y$ in $x = 7.3\overline{714285} + 1.\overline{428571} y$ with $- 2.5\overline{259}$ .

$x = 7.3\overline{714285} + 1.\overline{428571} (- 2.5\overline{259})$

$y = - 2.5\overline{259}$

Simplify the right side.

Simplify $7.3\overline{714285} + 1.\overline{428571} (- 2.5\overline{259})$ .

Multiply $1.\overline{428571}$ by $- 2.5\overline{259}$ .

$x = 7.3\overline{714285} - 3.\overline{608465}$

$y = - 2.5\overline{259}$

Subtract $3.\overline{608465}$ from $7.3\overline{714285}$ .

$x = 3.7\overline{629}$

$y = - 2.5\overline{259}$

$x = 3.7\overline{629}$

$y = - 2.5\overline{259}$

$x = 3.7\overline{629}$

$y = - 2.5\overline{259}$

$x = 3.7\overline{629}$

$y = - 2.5\overline{259}$

Step 5

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

$(3.7\overline{629}, - 2.5\overline{259})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(3.7\overline{629}, - 2.5\overline{259})$

Equation Form:

$x = 3.7\overline{629}, y = - 2.5\overline{259}$

Step 7

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