Precalculus Examples

$4 x + 3 y + 2 = 0$ , $6 y = 8 x + 28$

Step 1

Divide each term in $6 y = 8 x + 28$ by $6$ and simplify.

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Step 1.1

Divide each term in $6 y = 8 x + 28$ by $6$ .

$\frac{6 y}{6} = \frac{8 x}{6} + \frac{28}{6}$

$4 x + 3 y + 2 = 0$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $6$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{6 y}{6} = \frac{8 x}{6} + \frac{28}{6}$

$4 x + 3 y + 2 = 0$

Step 1.2.1.2

Divide $y$ by $1$ .

$y = \frac{8 x}{6} + \frac{28}{6}$

$4 x + 3 y + 2 = 0$

$y = \frac{8 x}{6} + \frac{28}{6}$

$4 x + 3 y + 2 = 0$

$y = \frac{8 x}{6} + \frac{28}{6}$

$4 x + 3 y + 2 = 0$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Cancel the common factor of $8$ and $6$ .

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Step 1.3.1.1.1

Factor $2$ out of $8 x$ .

$y = \frac{2 (4 x)}{6} + \frac{28}{6}$

$4 x + 3 y + 2 = 0$

Step 1.3.1.1.2

Cancel the common factors.

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Step 1.3.1.1.2.1

Factor $2$ out of $6$ .

$y = \frac{2 (4 x)}{2 (3)} + \frac{28}{6}$

$4 x + 3 y + 2 = 0$

Step 1.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 (4 x)}{2 \cdot 3} + \frac{28}{6}$

$4 x + 3 y + 2 = 0$

Step 1.3.1.1.2.3

Rewrite the expression.

$y = \frac{4 x}{3} + \frac{28}{6}$

$4 x + 3 y + 2 = 0$

$y = \frac{4 x}{3} + \frac{28}{6}$

$4 x + 3 y + 2 = 0$

$y = \frac{4 x}{3} + \frac{28}{6}$

$4 x + 3 y + 2 = 0$

Step 1.3.1.2

Cancel the common factor of $28$ and $6$ .

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Step 1.3.1.2.1

Factor $2$ out of $28$ .

$y = \frac{4 x}{3} + \frac{2 (14)}{6}$

$4 x + 3 y + 2 = 0$

Step 1.3.1.2.2

Cancel the common factors.

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Step 1.3.1.2.2.1

Factor $2$ out of $6$ .

$y = \frac{4 x}{3} + \frac{2 \cdot 14}{2 \cdot 3}$

$4 x + 3 y + 2 = 0$

Step 1.3.1.2.2.2

Cancel the common factor.

$y = \frac{4 x}{3} + \frac{2 \cdot 14}{2 \cdot 3}$

$4 x + 3 y + 2 = 0$

Step 1.3.1.2.2.3

Rewrite the expression.

$y = \frac{4 x}{3} + \frac{14}{3}$

$4 x + 3 y + 2 = 0$

$y = \frac{4 x}{3} + \frac{14}{3}$

$4 x + 3 y + 2 = 0$

$y = \frac{4 x}{3} + \frac{14}{3}$

$4 x + 3 y + 2 = 0$

$y = \frac{4 x}{3} + \frac{14}{3}$

$4 x + 3 y + 2 = 0$

$y = \frac{4 x}{3} + \frac{14}{3}$

$4 x + 3 y + 2 = 0$

$y = \frac{4 x}{3} + \frac{14}{3}$

$4 x + 3 y + 2 = 0$

Step 2

Replace all occurrences of $y$ with $\frac{4 x}{3} + \frac{14}{3}$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $4 x + 3 y + 2 = 0$ with $\frac{4 x}{3} + \frac{14}{3}$ .

$4 x + 3 (\frac{4 x}{3} + \frac{14}{3}) + 2 = 0$

$y = \frac{4 x}{3} + \frac{14}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $4 x + 3 (\frac{4 x}{3} + \frac{14}{3}) + 2$ .

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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.

$4 x + 3 (\frac{4 x}{3}) + 3 (\frac{14}{3}) + 2 = 0$

$y = \frac{4 x}{3} + \frac{14}{3}$

Step 2.2.1.1.2

Cancel the common factor of $3$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

$4 x + 3 (\frac{4 x}{3}) + 3 (\frac{14}{3}) + 2 = 0$

$y = \frac{4 x}{3} + \frac{14}{3}$

Step 2.2.1.1.2.2

Rewrite the expression.

$4 x + 4 x + 3 (\frac{14}{3}) + 2 = 0$

$y = \frac{4 x}{3} + \frac{14}{3}$

$4 x + 4 x + 3 (\frac{14}{3}) + 2 = 0$

$y = \frac{4 x}{3} + \frac{14}{3}$

Step 2.2.1.1.3

Cancel the common factor of $3$ .

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Step 2.2.1.1.3.1

Cancel the common factor.

$4 x + 4 x + 3 (\frac{14}{3}) + 2 = 0$

$y = \frac{4 x}{3} + \frac{14}{3}$

Step 2.2.1.1.3.2

Rewrite the expression.

$4 x + 4 x + 14 + 2 = 0$

$y = \frac{4 x}{3} + \frac{14}{3}$

$4 x + 4 x + 14 + 2 = 0$

$y = \frac{4 x}{3} + \frac{14}{3}$

$4 x + 4 x + 14 + 2 = 0$

$y = \frac{4 x}{3} + \frac{14}{3}$

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Add $4 x$ and $4 x$ .

$8 x + 14 + 2 = 0$

$y = \frac{4 x}{3} + \frac{14}{3}$

Step 2.2.1.2.2

Add $14$ and $2$ .

$8 x + 16 = 0$

$y = \frac{4 x}{3} + \frac{14}{3}$

$8 x + 16 = 0$

$y = \frac{4 x}{3} + \frac{14}{3}$

$8 x + 16 = 0$

$y = \frac{4 x}{3} + \frac{14}{3}$

$8 x + 16 = 0$

$y = \frac{4 x}{3} + \frac{14}{3}$

$8 x + 16 = 0$

$y = \frac{4 x}{3} + \frac{14}{3}$

Step 3

Solve for $x$ in $8 x + 16 = 0$ .

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Step 3.1

Subtract $16$ from both sides of the equation.

$8 x = - 16$

$y = \frac{4 x}{3} + \frac{14}{3}$

Step 3.2

Divide each term in $8 x = - 16$ by $8$ and simplify.

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Step 3.2.1

Divide each term in $8 x = - 16$ by $8$ .

$\frac{8 x}{8} = \frac{- 16}{8}$

$y = \frac{4 x}{3} + \frac{14}{3}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $8$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{- 16}{8}$

$y = \frac{4 x}{3} + \frac{14}{3}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 16}{8}$

$y = \frac{4 x}{3} + \frac{14}{3}$

$x = \frac{- 16}{8}$

$y = \frac{4 x}{3} + \frac{14}{3}$

$x = \frac{- 16}{8}$

$y = \frac{4 x}{3} + \frac{14}{3}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $- 16$ by $8$ .

$x = - 2$

$y = \frac{4 x}{3} + \frac{14}{3}$

$x = - 2$

$y = \frac{4 x}{3} + \frac{14}{3}$

$x = - 2$

$y = \frac{4 x}{3} + \frac{14}{3}$

$x = - 2$

$y = \frac{4 x}{3} + \frac{14}{3}$

Step 4

Replace all occurrences of $x$ with $- 2$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $y = \frac{4 x}{3} + \frac{14}{3}$ with $- 2$ .

$y = \frac{4 (- 2)}{3} + \frac{14}{3}$

$x = - 2$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{4 (- 2)}{3} + \frac{14}{3}$ .

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Step 4.2.1.1

Combine the numerators over the common denominator.

$y = \frac{4 (- 2) + 14}{3}$

$x = - 2$

Step 4.2.1.2

Simplify the expression.

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Step 4.2.1.2.1

Multiply $4$ by $- 2$ .

$y = \frac{- 8 + 14}{3}$

$x = - 2$

Step 4.2.1.2.2

Add $- 8$ and $14$ .

$y = \frac{6}{3}$

$x = - 2$

Step 4.2.1.2.3

Divide $6$ by $3$ .

$y = 2$

$x = - 2$

$y = 2$

$x = - 2$

$y = 2$

$x = - 2$

$y = 2$

$x = - 2$

$y = 2$

$x = - 2$

Step 5

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

$(- 2, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 2, 2)$

Equation Form:

$x = - 2, y = 2$

Step 7