Algebra Examples

$x + y = - 5$ $y = 5 x + 1$

Step 1

Replace all occurrences of $y$ with $5 x + 1$ in each equation.

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Step 1.1

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

$x + 5 x + 1 = - 5$

$y = 5 x + 1$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $x + 5 x + 1$ .

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Step 1.2.1.1

Remove parentheses.

$x + 5 x + 1 = - 5$

$y = 5 x + 1$

Step 1.2.1.2

Add $x$ and $5 x$ .

$6 x + 1 = - 5$

$y = 5 x + 1$

$6 x + 1 = - 5$

$y = 5 x + 1$

$6 x + 1 = - 5$

$y = 5 x + 1$

$6 x + 1 = - 5$

$y = 5 x + 1$

Step 2

Solve for $x$ in $6 x + 1 = - 5$ .

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Step 2.1

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

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Step 2.1.1

Subtract $1$ from both sides of the equation.

$6 x = - 5 - 1$

$y = 5 x + 1$

Step 2.1.2

Subtract $1$ from $- 5$ .

$6 x = - 6$

$y = 5 x + 1$

$6 x = - 6$

$y = 5 x + 1$

Step 2.2

Divide each term in $6 x = - 6$ by $6$ and simplify.

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Step 2.2.1

Divide each term in $6 x = - 6$ by $6$ .

$\frac{6 x}{6} = \frac{- 6}{6}$

$y = 5 x + 1$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $6$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 6}{6}$

$y = 5 x + 1$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 6}{6}$

$y = 5 x + 1$

$x = \frac{- 6}{6}$

$y = 5 x + 1$

$x = \frac{- 6}{6}$

$y = 5 x + 1$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $- 6$ by $6$ .

$x = - 1$

$y = 5 x + 1$

$x = - 1$

$y = 5 x + 1$

$x = - 1$

$y = 5 x + 1$

$x = - 1$

$y = 5 x + 1$

Step 3

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

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Step 3.1

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

$y = 5 (- 1) + 1$

$x = - 1$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $5 (- 1) + 1$ .

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Step 3.2.1.1

Multiply $5$ by $- 1$ .

$y = - 5 + 1$

$x = - 1$

Step 3.2.1.2

Add $- 5$ and $1$ .

$y = - 4$

$x = - 1$

$y = - 4$

$x = - 1$

$y = - 4$

$x = - 1$

$y = - 4$

$x = - 1$

Step 4

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

$(- 1, - 4)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 1, - 4)$

Equation Form:

$x = - 1, y = - 4$

Step 6