Algebra Examples

$- x - y = - 9$ and $- 3 x - 2 y = - 28$

Step 1

Solve for $x$ in $- x - y = - 9$ .

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Step 1.1

Add $y$ to both sides of the equation.

$- x = - 9 + y$

$- 3 x - 2 y = - 28$

Step 1.2

Divide each term in $- x = - 9 + y$ by $- 1$ and simplify.

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Step 1.2.1

Divide each term in $- x = - 9 + y$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 9}{- 1} + \frac{y}{- 1}$

$- 3 x - 2 y = - 28$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 9}{- 1} + \frac{y}{- 1}$

$- 3 x - 2 y = - 28$

Step 1.2.2.2

Divide $x$ by $1$ .

$x = \frac{- 9}{- 1} + \frac{y}{- 1}$

$- 3 x - 2 y = - 28$

$x = \frac{- 9}{- 1} + \frac{y}{- 1}$

$- 3 x - 2 y = - 28$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Divide $- 9$ by $- 1$ .

$x = 9 + \frac{y}{- 1}$

$- 3 x - 2 y = - 28$

Step 1.2.3.1.2

Move the negative one from the denominator of $\frac{y}{- 1}$ .

$x = 9 - 1 \cdot y$

$- 3 x - 2 y = - 28$

Step 1.2.3.1.3

Rewrite $- 1 \cdot y$ as $- y$ .

$x = 9 - y$

$- 3 x - 2 y = - 28$

$x = 9 - y$

$- 3 x - 2 y = - 28$

$x = 9 - y$

$- 3 x - 2 y = - 28$

$x = 9 - y$

$- 3 x - 2 y = - 28$

$x = 9 - y$

$- 3 x - 2 y = - 28$

Step 2

Replace all occurrences of $x$ with $9 - y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- 3 x - 2 y = - 28$ with $9 - y$ .

$- 3 (9 - y) - 2 y = - 28$

$x = 9 - y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 3 (9 - y) - 2 y$ .

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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.

$- 3 \cdot 9 - 3 (- y) - 2 y = - 28$

$x = 9 - y$

Step 2.2.1.1.2

Multiply $- 3$ by $9$ .

$- 27 - 3 (- y) - 2 y = - 28$

$x = 9 - y$

Step 2.2.1.1.3

Multiply $- 1$ by $- 3$ .

$- 27 + 3 y - 2 y = - 28$

$x = 9 - y$

$- 27 + 3 y - 2 y = - 28$

$x = 9 - y$

Step 2.2.1.2

Subtract $2 y$ from $3 y$ .

$- 27 + y = - 28$

$x = 9 - y$

$- 27 + y = - 28$

$x = 9 - y$

$- 27 + y = - 28$

$x = 9 - y$

$- 27 + y = - 28$

$x = 9 - y$

Step 3

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

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Step 3.1

Add $27$ to both sides of the equation.

$y = - 28 + 27$

$x = 9 - y$

Step 3.2

Add $- 28$ and $27$ .

$y = - 1$

$x = 9 - y$

$y = - 1$

$x = 9 - y$

Step 4

Replace all occurrences of $y$ with $- 1$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = 9 - y$ with $- 1$ .

$x = 9 - (- 1)$

$y = - 1$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $9 - (- 1)$ .

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Step 4.2.1.1

Multiply $- 1$ by $- 1$ .

$x = 9 + 1$

$y = - 1$

Step 4.2.1.2

Add $9$ and $1$ .

$x = 10$

$y = - 1$

$x = 10$

$y = - 1$

$x = 10$

$y = - 1$

$x = 10$

$y = - 1$

Step 5

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

$(10, - 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(10, - 1)$

Equation Form:

$x = 10, y = - 1$

Step 7