Algebra Examples

$2.4 (x + 4 y) = - 4.8$ $2.4 x - 9 y = - 14.1$

Step 1

Solve for $x$ in $2.4 (x + 4 y) = - 4.8$ .

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Step 1.1

Divide each term in $2.4 (x + 4 y) = - 4.8$ by $2.4$ and simplify.

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Step 1.1.1

Divide each term in $2.4 (x + 4 y) = - 4.8$ by $2.4$ .

$\frac{2.4 (x + 4 y)}{2.4} = \frac{- 4.8}{2.4}$

$2.4 x - 9 y = - 14.1$

Step 1.1.2

Simplify the left side.

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Step 1.1.2.1

Cancel the common factor of $2.4$ .

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Step 1.1.2.1.1

Cancel the common factor.

$\frac{2.4 (x + 4 y)}{2.4} = \frac{- 4.8}{2.4}$

$2.4 x - 9 y = - 14.1$

Step 1.1.2.1.2

Divide $x + 4 y$ by $1$ .

$x + 4 y = \frac{- 4.8}{2.4}$

$2.4 x - 9 y = - 14.1$

$x + 4 y = \frac{- 4.8}{2.4}$

$2.4 x - 9 y = - 14.1$

$x + 4 y = \frac{- 4.8}{2.4}$

$2.4 x - 9 y = - 14.1$

Step 1.1.3

Simplify the right side.

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Step 1.1.3.1

Divide $- 4.8$ by $2.4$ .

$x + 4 y = - 2$

$2.4 x - 9 y = - 14.1$

$x + 4 y = - 2$

$2.4 x - 9 y = - 14.1$

$x + 4 y = - 2$

$2.4 x - 9 y = - 14.1$

Step 1.2

Subtract $4 y$ from both sides of the equation.

$x = - 2 - 4 y$

$2.4 x - 9 y = - 14.1$

$x = - 2 - 4 y$

$2.4 x - 9 y = - 14.1$

Step 2

Replace all occurrences of $x$ with $- 2 - 4 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $2.4 x - 9 y = - 14.1$ with $- 2 - 4 y$ .

$2.4 (- 2 - 4 y) - 9 y = - 14.1$

$x = - 2 - 4 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $2.4 (- 2 - 4 y) - 9 y$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$2.4 \cdot - 2 + 2.4 (- 4 y) - 9 y = - 14.1$

$x = - 2 - 4 y$

Step 2.2.1.1.2

Multiply $2.4$ by $- 2$ .

$- 4.8 + 2.4 (- 4 y) - 9 y = - 14.1$

$x = - 2 - 4 y$

Step 2.2.1.1.3

Multiply $- 4$ by $2.4$ .

$- 4.8 - 9.6 y - 9 y = - 14.1$

$x = - 2 - 4 y$

$- 4.8 - 9.6 y - 9 y = - 14.1$

$x = - 2 - 4 y$

Step 2.2.1.2

Subtract $9 y$ from $- 9.6 y$ .

$- 4.8 - 18.6 y = - 14.1$

$x = - 2 - 4 y$

$- 4.8 - 18.6 y = - 14.1$

$x = - 2 - 4 y$

$- 4.8 - 18.6 y = - 14.1$

$x = - 2 - 4 y$

$- 4.8 - 18.6 y = - 14.1$

$x = - 2 - 4 y$

Step 3

Solve for $y$ in $- 4.8 - 18.6 y = - 14.1$ .

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Step 3.1

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

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Step 3.1.1

Add $4.8$ to both sides of the equation.

$- 18.6 y = - 14.1 + 4.8$

$x = - 2 - 4 y$

Step 3.1.2

Add $- 14.1$ and $4.8$ .

$- 18.6 y = - 9.3$

$x = - 2 - 4 y$

$- 18.6 y = - 9.3$

$x = - 2 - 4 y$

Step 3.2

Divide each term in $- 18.6 y = - 9.3$ by $- 18.6$ and simplify.

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Step 3.2.1

Divide each term in $- 18.6 y = - 9.3$ by $- 18.6$ .

$\frac{- 18.6 y}{- 18.6} = \frac{- 9.3}{- 18.6}$

$x = - 2 - 4 y$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 18.6$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 18.6 y}{- 18.6} = \frac{- 9.3}{- 18.6}$

$x = - 2 - 4 y$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 9.3}{- 18.6}$

$x = - 2 - 4 y$

$y = \frac{- 9.3}{- 18.6}$

$x = - 2 - 4 y$

$y = \frac{- 9.3}{- 18.6}$

$x = - 2 - 4 y$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $- 9.3$ by $- 18.6$ .

$y = 0.5$

$x = - 2 - 4 y$

$y = 0.5$

$x = - 2 - 4 y$

$y = 0.5$

$x = - 2 - 4 y$

$y = 0.5$

$x = - 2 - 4 y$

Step 4

Replace all occurrences of $y$ with $0.5$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = - 2 - 4 y$ with $0.5$ .

$x = - 2 - 4 \cdot 0.5$

$y = 0.5$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- 2 - 4 \cdot 0.5$ .

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Step 4.2.1.1

Multiply $- 4$ by $0.5$ .

$x = - 2 - 2$

$y = 0.5$

Step 4.2.1.2

Subtract $2$ from $- 2$ .

$x = - 4$

$y = 0.5$

$x = - 4$

$y = 0.5$

$x = - 4$

$y = 0.5$

$x = - 4$

$y = 0.5$

Step 5

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

$(- 4, 0.5)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 4, 0.5)$

Equation Form:

$x = - 4, y = 0.5$

Step 7