Algebra Examples

$y = - 4 x$ $y = x - 5$

Step 1

Eliminate the equal sides of each equation and combine.

$- 4 x = x - 5$

Step 2

Solve $- 4 x = x - 5$ for $x$ .

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Step 2.1

Move all terms containing $x$ to the left side of the equation.

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Step 2.1.1

Subtract $x$ from both sides of the equation.

$- 4 x - x = - 5$

Step 2.1.2

Subtract $x$ from $- 4 x$ .

$- 5 x = - 5$

Step 2.2

Divide each term in $- 5 x = - 5$ by $- 5$ and simplify.

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Step 2.2.1

Divide each term in $- 5 x = - 5$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 5}{- 5}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $- 5$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 5}{- 5}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 5}{- 5}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $- 5$ by $- 5$ .

$x = 1$

Step 3

Evaluate $y$ when $x = 1$ .

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Step 3.1

Substitute $1$ for $x$ .

$y = (1) - 5$

Step 3.2

Substitute $1$ for $x$ in $y = (1) - 5$ and solve for $y$ .

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Step 3.2.1

Remove parentheses.

$y = 1 - 5$

Step 3.2.2

Remove parentheses.

$y = (1) - 5$

Step 3.2.3

Subtract $5$ from $1$ .

$y = - 4$

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