Find the Points of Intersection -0.1x-0.8y=2 0.6x-0.5y=-1.4

$- 0.1 x - 0.8 y = 2$ $0.6 x - 0.5 y = - 1.4$

Step 1

Solve for $x$ in $- 0.1 x - 0.8 y = 2$ .

Add $0.8 y$ to both sides of the equation.

$- 0.1 x = 2 + 0.8 y$

$0.6 x - 0.5 y = - 1.4$

Divide each term in $- 0.1 x = 2 + 0.8 y$ by $- 0.1$ and simplify.

Divide each term in $- 0.1 x = 2 + 0.8 y$ by $- 0.1$ .

$\frac{- 0.1 x}{- 0.1} = \frac{2}{- 0.1} + \frac{0.8 y}{- 0.1}$

$0.6 x - 0.5 y = - 1.4$

Simplify the left side.

Cancel the common factor of $- 0.1$ .

Cancel the common factor.

$\frac{- 0.1 x}{- 0.1} = \frac{2}{- 0.1} + \frac{0.8 y}{- 0.1}$

$0.6 x - 0.5 y = - 1.4$

Divide $x$ by $1$ .

$x = \frac{2}{- 0.1} + \frac{0.8 y}{- 0.1}$

$0.6 x - 0.5 y = - 1.4$

$x = \frac{2}{- 0.1} + \frac{0.8 y}{- 0.1}$

$0.6 x - 0.5 y = - 1.4$

$x = \frac{2}{- 0.1} + \frac{0.8 y}{- 0.1}$

$0.6 x - 0.5 y = - 1.4$

Simplify the right side.

Simplify each term.

Divide $2$ by $- 0.1$ .

$x = - 20 + \frac{0.8 y}{- 0.1}$

$0.6 x - 0.5 y = - 1.4$

Move the negative in front of the fraction.

$x = - 20 - \frac{0.8 y}{0.1}$

$0.6 x - 0.5 y = - 1.4$

Factor $0.8$ out of $0.8 y$ .

$x = - 20 - \frac{0.8 (y)}{0.1}$

$0.6 x - 0.5 y = - 1.4$

Factor $0.1$ out of $0.1$ .

$x = - 20 - \frac{0.8 (y)}{0.1 (1)}$

$0.6 x - 0.5 y = - 1.4$

Separate fractions.

$x = - 20 - (\frac{0.8}{0.1} \cdot \frac{y}{1})$

$0.6 x - 0.5 y = - 1.4$

Divide $0.8$ by $0.1$ .

$x = - 20 - (8 (\frac{y}{1}))$

$0.6 x - 0.5 y = - 1.4$

Divide $y$ by $1$ .

$x = - 20 - (8 y)$

$0.6 x - 0.5 y = - 1.4$

Multiply $8$ by $- 1$ .

$x = - 20 - 8 y$

$0.6 x - 0.5 y = - 1.4$

$x = - 20 - 8 y$

$0.6 x - 0.5 y = - 1.4$

$x = - 20 - 8 y$

$0.6 x - 0.5 y = - 1.4$

$x = - 20 - 8 y$

$0.6 x - 0.5 y = - 1.4$

$x = - 20 - 8 y$

$0.6 x - 0.5 y = - 1.4$

Step 2

Replace all occurrences of $x$ with $- 20 - 8 y$ in each equation.

Replace all occurrences of $x$ in $0.6 x - 0.5 y = - 1.4$ with $- 20 - 8 y$ .

$0.6 (- 20 - 8 y) - 0.5 y = - 1.4$

$x = - 20 - 8 y$

Simplify the left side.

Simplify $0.6 (- 20 - 8 y) - 0.5 y$ .

Simplify each term.

Apply the distributive property.

$0.6 \cdot - 20 + 0.6 (- 8 y) - 0.5 y = - 1.4$

$x = - 20 - 8 y$

Multiply $0.6$ by $- 20$ .

$- 12 + 0.6 (- 8 y) - 0.5 y = - 1.4$

$x = - 20 - 8 y$

Multiply $- 8$ by $0.6$ .

$- 12 - 4.8 y - 0.5 y = - 1.4$

$x = - 20 - 8 y$

$- 12 - 4.8 y - 0.5 y = - 1.4$

$x = - 20 - 8 y$

Subtract $0.5 y$ from $- 4.8 y$ .

$- 12 - 5.3 y = - 1.4$

$x = - 20 - 8 y$

$- 12 - 5.3 y = - 1.4$

$x = - 20 - 8 y$

$- 12 - 5.3 y = - 1.4$

$x = - 20 - 8 y$

$- 12 - 5.3 y = - 1.4$

$x = - 20 - 8 y$

Step 3

Solve for $y$ in $- 12 - 5.3 y = - 1.4$ .

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

Add $12$ to both sides of the equation.

$- 5.3 y = - 1.4 + 12$

$x = - 20 - 8 y$

Add $- 1.4$ and $12$ .

$- 5.3 y = 10.6$

$x = - 20 - 8 y$

$- 5.3 y = 10.6$

$x = - 20 - 8 y$

Divide each term in $- 5.3 y = 10.6$ by $- 5.3$ and simplify.

Divide each term in $- 5.3 y = 10.6$ by $- 5.3$ .

$\frac{- 5.3 y}{- 5.3} = \frac{10.6}{- 5.3}$

$x = - 20 - 8 y$

Simplify the left side.

Cancel the common factor of $- 5.3$ .

Cancel the common factor.

$\frac{- 5.3 y}{- 5.3} = \frac{10.6}{- 5.3}$

$x = - 20 - 8 y$

Divide $y$ by $1$ .

$y = \frac{10.6}{- 5.3}$

$x = - 20 - 8 y$

$y = \frac{10.6}{- 5.3}$

$x = - 20 - 8 y$

$y = \frac{10.6}{- 5.3}$

$x = - 20 - 8 y$

Simplify the right side.

Divide $10.6$ by $- 5.3$ .

$y = - 2$

$x = - 20 - 8 y$

$y = - 2$

$x = - 20 - 8 y$

$y = - 2$

$x = - 20 - 8 y$

$y = - 2$

$x = - 20 - 8 y$

Step 4

Replace all occurrences of $y$ with $- 2$ in each equation.

Replace all occurrences of $y$ in $x = - 20 - 8 y$ with $- 2$ .

$x = - 20 - 8 \cdot - 2$

$y = - 2$

Simplify the right side.

Simplify $- 20 - 8 \cdot - 2$ .

Multiply $- 8$ by $- 2$ .

$x = - 20 + 16$

$y = - 2$

Add $- 20$ and $16$ .

$x = - 4$

$y = - 2$

$x = - 4$

$y = - 2$

$x = - 4$

$y = - 2$

$x = - 4$

$y = - 2$

Step 5

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

$(- 4, - 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 4, - 2)$

Equation Form:

$x = - 4, y = - 2$

Step 7

Find the Points of Intersection -0.1x-0.8y=2 0.6x-0.5y=-1.4

Related Questions

Support LCMGCF.com by disabling your adblocker.