Trigonometry Examples

$\frac{1}{2} x - \frac{1}{3} y = 1$ , $y = - 3$

Step 1

Replace all occurrences of $y$ with $- 3$ in each equation.

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Step 1.1

Replace all occurrences of $y$ in $\frac{1}{2} x - \frac{1}{3} y = 1$ with $- 3$ .

$\frac{1}{2} x - \frac{1}{3} \cdot - 3 = 1$

$y = - 3$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Combine $\frac{1}{2}$ and $x$ .

$\frac{x}{2} - \frac{1}{3} \cdot - 3 = 1$

$y = - 3$

Step 1.2.1.2

Cancel the common factor of $3$ .

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Step 1.2.1.2.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$\frac{x}{2} + \frac{- 1}{3} \cdot - 3 = 1$

$y = - 3$

Step 1.2.1.2.2

Factor $3$ out of $- 3$ .

$\frac{x}{2} + \frac{- 1}{3} \cdot (3 (- 1)) = 1$

$y = - 3$

Step 1.2.1.2.3

Cancel the common factor.

$\frac{x}{2} + \frac{- 1}{3} \cdot (3 \cdot - 1) = 1$

$y = - 3$

Step 1.2.1.2.4

Rewrite the expression.

$\frac{x}{2} - 1 \cdot - 1 = 1$

$y = - 3$

$\frac{x}{2} - 1 \cdot - 1 = 1$

$y = - 3$

Step 1.2.1.3

Multiply $- 1$ by $- 1$ .

$\frac{x}{2} + 1 = 1$

$y = - 3$

$\frac{x}{2} + 1 = 1$

$y = - 3$

$\frac{x}{2} + 1 = 1$

$y = - 3$

$\frac{x}{2} + 1 = 1$

$y = - 3$

Step 2

Solve for $x$ in $\frac{x}{2} + 1 = 1$ .

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Step 2.1

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

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Step 2.1.1

Subtract $1$ from both sides of the equation.

$\frac{x}{2} = 1 - 1$

$y = - 3$

Step 2.1.2

Subtract $1$ from $1$ .

$\frac{x}{2} = 0$

$y = - 3$

$\frac{x}{2} = 0$

$y = - 3$

Step 2.2

Set the numerator equal to zero.

$x = 0$

$y = - 3$

$x = 0$

$y = - 3$

Step 3

Solve the system of equations.

$x = 0 y = - 3$

Step 4

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

$(0, - 3)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(0, - 3)$

Equation Form:

$x = 0, y = - 3$

Step 6