Algebra Examples

$x - y = - 1$ and $- 5 x + 3 y = - 15$

Step 1

Add $y$ to both sides of the equation.

$x = - 1 + y$

$- 5 x + 3 y = - 15$

Step 2

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

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Step 2.1

Replace all occurrences of $x$ in $- 5 x + 3 y = - 15$ with $- 1 + y$ .

$- 5 (- 1 + y) + 3 y = - 15$

$x = - 1 + y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 5 (- 1 + y) + 3 y$ .

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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.

$- 5 \cdot - 1 - 5 y + 3 y = - 15$

$x = - 1 + y$

Step 2.2.1.1.2

Multiply $- 5$ by $- 1$ .

$5 - 5 y + 3 y = - 15$

$x = - 1 + y$

$5 - 5 y + 3 y = - 15$

$x = - 1 + y$

Step 2.2.1.2

Add $- 5 y$ and $3 y$ .

$5 - 2 y = - 15$

$x = - 1 + y$

$5 - 2 y = - 15$

$x = - 1 + y$

$5 - 2 y = - 15$

$x = - 1 + y$

$5 - 2 y = - 15$

$x = - 1 + y$

Step 3

Solve for $y$ in $5 - 2 y = - 15$ .

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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

Subtract $5$ from both sides of the equation.

$- 2 y = - 15 - 5$

$x = - 1 + y$

Step 3.1.2

Subtract $5$ from $- 15$ .

$- 2 y = - 20$

$x = - 1 + y$

$- 2 y = - 20$

$x = - 1 + y$

Step 3.2

Divide each term in $- 2 y = - 20$ by $- 2$ and simplify.

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Step 3.2.1

Divide each term in $- 2 y = - 20$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 20}{- 2}$

$x = - 1 + y$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 20}{- 2}$

$x = - 1 + y$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 20}{- 2}$

$x = - 1 + y$

$y = \frac{- 20}{- 2}$

$x = - 1 + y$

$y = \frac{- 20}{- 2}$

$x = - 1 + y$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $- 20$ by $- 2$ .

$y = 10$

$x = - 1 + y$

$y = 10$

$x = - 1 + y$

$y = 10$

$x = - 1 + y$

$y = 10$

$x = - 1 + y$

Step 4

Replace all occurrences of $y$ with $10$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = - 1 + y$ with $10$ .

$x = - 1 + 10$

$y = 10$

Step 4.2

Simplify $x = - 1 + 10$ .

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Remove parentheses.

$x = - 1 + 10$

$y = 10$

$x = - 1 + 10$

$y = 10$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Add $- 1$ and $10$ .

$x = 9$

$y = 10$

$x = 9$

$y = 10$

$x = 9$

$y = 10$

$x = 9$

$y = 10$

Step 5

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

$(9, 10)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(9, 10)$

Equation Form:

$x = 9, y = 10$

Step 7