Algebra Examples

$y = x + 5$ $y = - 2 x - 1$

Step 1

Eliminate the equal sides of each equation and combine.

$x + 5 = - 2 x - 1$

Step 2

Solve $x + 5 = - 2 x - 1$ for $x$ .

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

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Add $2 x$ to both sides of the equation.

$x + 5 + 2 x = - 1$

Add $x$ and $2 x$ .

$3 x + 5 = - 1$

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

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Subtract $5$ from both sides of the equation.

$3 x = - 1 - 5$

Subtract $5$ from $- 1$ .

$3 x = - 6$

Divide each term in $3 x = - 6$ by $3$ and simplify.

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Divide each term in $3 x = - 6$ by $3$ .

$\frac{3 x}{3} = \frac{- 6}{3}$

Simplify the left side.

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Cancel the common factor of $3$ .

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Cancel the common factor.

$\frac{3 x}{3} = \frac{- 6}{3}$

Divide $x$ by $1$ .

$x = \frac{- 6}{3}$

Simplify the right side.

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Divide $- 6$ by $3$ .

$x = - 2$

Step 3

Evaluate $y$ when $x = - 2$ .

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Substitute $- 2$ for $x$ .

$y = - 2 \cdot - 2 - 1$

Substitute $- 2$ for $x$ in $y = - 2 \cdot - 2 - 1$ and solve for $y$ .

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Remove parentheses.

$y = - 2 \cdot - 2 - 1$

Simplify $- 2 \cdot - 2 - 1$ .

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Multiply $- 2$ by $- 2$ .

$y = 4 - 1$

Subtract $1$ from $4$ .

$y = 3$

Step 4

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

$(- 2, 3)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 2, 3)$

Equation Form:

$x = - 2, y = 3$

Step 6