Algebra Examples

$y = 4 x + 3$ and $y = - x - 2$

Step 1

Eliminate the equal sides of each equation and combine.

$4 x + 3 = - x - 2$

Step 2

Solve $4 x + 3 = - x - 2$ 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

Add $x$ to both sides of the equation.

$4 x + 3 + x = - 2$

Step 2.1.2

Add $4 x$ and $x$ .

$5 x + 3 = - 2$

Step 2.2

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

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Step 2.2.1

Subtract $3$ from both sides of the equation.

$5 x = - 2 - 3$

Step 2.2.2

Subtract $3$ from $- 2$ .

$5 x = - 5$

Step 2.3

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

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Step 2.3.1

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

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

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $5$ .

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Step 2.3.2.1.1

Cancel the common factor.

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

Step 2.3.2.1.2

Divide $x$ by $1$ .

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

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $- 5$ by $5$ .

$x = - 1$

Step 3

Evaluate $y$ when $x = - 1$ .

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Step 3.1

Substitute $- 1$ for $x$ .

$y = - (- 1) - 2$

Step 3.2

Simplify $- (- 1) - 2$ .

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Step 3.2.1

Multiply $- 1$ by $- 1$ .

$y = 1 - 2$

Step 3.2.2

Subtract $2$ from $1$ .

$y = - 1$

Step 4

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

$(- 1, - 1)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 1, - 1)$

Equation Form:

$x = - 1, y = - 1$

Step 6