Precalculus Examples

$y + x = 9$ , $3 y = 2 x + 8$

Step 1

Subtract $x$ from both sides of the equation.

$y = 9 - x$

$3 y = 2 x + 8$

Step 2

Replace all occurrences of $y$ with $9 - x$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $3 y = 2 x + 8$ with $9 - x$ .

$3 (9 - x) = 2 x + 8$

$y = 9 - x$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $3 (9 - x)$ .

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Step 2.2.1.1

Apply the distributive property.

$3 \cdot 9 + 3 (- x) = 2 x + 8$

$y = 9 - x$

Step 2.2.1.2

Multiply.

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Step 2.2.1.2.1

Multiply $3$ by $9$ .

$27 + 3 (- x) = 2 x + 8$

$y = 9 - x$

Step 2.2.1.2.2

Multiply $- 1$ by $3$ .

$27 - 3 x = 2 x + 8$

$y = 9 - x$

$27 - 3 x = 2 x + 8$

$y = 9 - x$

$27 - 3 x = 2 x + 8$

$y = 9 - x$

$27 - 3 x = 2 x + 8$

$y = 9 - x$

$27 - 3 x = 2 x + 8$

$y = 9 - x$

Step 3

Solve for $x$ in $27 - 3 x = 2 x + 8$ .

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Step 3.1

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

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Step 3.1.1

Subtract $2 x$ from both sides of the equation.

$27 - 3 x - 2 x = 8$

$y = 9 - x$

Step 3.1.2

Subtract $2 x$ from $- 3 x$ .

$27 - 5 x = 8$

$y = 9 - x$

$27 - 5 x = 8$

$y = 9 - x$

Step 3.2

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

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Step 3.2.1

Subtract $27$ from both sides of the equation.

$- 5 x = 8 - 27$

$y = 9 - x$

Step 3.2.2

Subtract $27$ from $8$ .

$- 5 x = - 19$

$y = 9 - x$

$- 5 x = - 19$

$y = 9 - x$

Step 3.3

Divide each term in $- 5 x = - 19$ by $- 5$ and simplify.

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Step 3.3.1

Divide each term in $- 5 x = - 19$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 19}{- 5}$

$y = 9 - x$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 5$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 19}{- 5}$

$y = 9 - x$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 19}{- 5}$

$y = 9 - x$

$x = \frac{- 19}{- 5}$

$y = 9 - x$

$x = \frac{- 19}{- 5}$

$y = 9 - x$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Dividing two negative values results in a positive value.

$x = \frac{19}{5}$

$y = 9 - x$

$x = \frac{19}{5}$

$y = 9 - x$

$x = \frac{19}{5}$

$y = 9 - x$

$x = \frac{19}{5}$

$y = 9 - x$

Step 4

Replace all occurrences of $x$ with $\frac{19}{5}$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $y = 9 - x$ with $\frac{19}{5}$ .

$y = 9 - (\frac{19}{5})$

$x = \frac{19}{5}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $9 - (\frac{19}{5})$ .

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Step 4.2.1.1

To write $9$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = 9 \cdot \frac{5}{5} - \frac{19}{5}$

$x = \frac{19}{5}$

Step 4.2.1.2

Combine $9$ and $\frac{5}{5}$ .

$y = \frac{9 \cdot 5}{5} - \frac{19}{5}$

$x = \frac{19}{5}$

Step 4.2.1.3

Combine the numerators over the common denominator.

$y = \frac{9 \cdot 5 - 19}{5}$

$x = \frac{19}{5}$

Step 4.2.1.4

Simplify the numerator.

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Step 4.2.1.4.1

Multiply $9$ by $5$ .

$y = \frac{45 - 19}{5}$

$x = \frac{19}{5}$

Step 4.2.1.4.2

Subtract $19$ from $45$ .

$y = \frac{26}{5}$

$x = \frac{19}{5}$

$y = \frac{26}{5}$

$x = \frac{19}{5}$

$y = \frac{26}{5}$

$x = \frac{19}{5}$

$y = \frac{26}{5}$

$x = \frac{19}{5}$

$y = \frac{26}{5}$

$x = \frac{19}{5}$

Step 5

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

$(\frac{19}{5}, \frac{26}{5})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(\frac{19}{5}, \frac{26}{5})$

Equation Form:

$x = \frac{19}{5}, y = \frac{26}{5}$

Step 7