Precalculus Examples

$12 x + k y = 5$ , $15 x - 10 y = - 11$

Step 1

Reduce the system.

$12 x + k (\frac{11}{10} + \frac{3 x}{2}) = 5, y = \frac{11}{10} + \frac{3 x}{2}$

Step 2

Simplify the left side.

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Step 2.1

Simplify $12 x + k (\frac{11}{10} + \frac{3 x}{2})$ .

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Apply the distributive property.

$12 x + k (\frac{11}{10}) + k (\frac{3 x}{2}) = 5$

$y = \frac{11}{10} + \frac{3 x}{2}$

Step 2.1.1.2

Combine $k$ and $\frac{11}{10}$ .

$12 x + \frac{k \cdot 11}{10} + k (\frac{3 x}{2}) = 5$

$y = \frac{11}{10} + \frac{3 x}{2}$

Step 2.1.1.3

Combine $k$ and $\frac{3 x}{2}$ .

$12 x + \frac{k \cdot 11}{10} + \frac{k (3 x)}{2} = 5$

$y = \frac{11}{10} + \frac{3 x}{2}$

Step 2.1.1.4

Simplify each term.

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Step 2.1.1.4.1

Move $11$ to the left of $k$ .

$12 x + \frac{11 \cdot k}{10} + \frac{k (3 x)}{2} = 5$

$y = \frac{11}{10} + \frac{3 x}{2}$

Step 2.1.1.4.2

Move $3$ to the left of $k$ .

$12 x + \frac{11 k}{10} + \frac{3 k x}{2} = 5$

$y = \frac{11}{10} + \frac{3 x}{2}$

$12 x + \frac{11 k}{10} + \frac{3 k x}{2} = 5$

$y = \frac{11}{10} + \frac{3 x}{2}$

$12 x + \frac{11 k}{10} + \frac{3 k x}{2} = 5$

$y = \frac{11}{10} + \frac{3 x}{2}$

Step 2.1.2

Simplify the expression.

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Step 2.1.2.1

Move $12 x$ .

$\frac{11 k}{10} + \frac{3 k x}{2} + 12 x = 5$

$y = \frac{11}{10} + \frac{3 x}{2}$

Step 2.1.2.2

Reorder $\frac{11 k}{10}$ and $\frac{3 k x}{2}$ .

$\frac{3 k x}{2} + \frac{11 k}{10} + 12 x = 5$

$y = \frac{11}{10} + \frac{3 x}{2}$

$\frac{3 k x}{2} + \frac{11 k}{10} + 12 x = 5$

$y = \frac{11}{10} + \frac{3 x}{2}$

$\frac{3 k x}{2} + \frac{11 k}{10} + 12 x = 5$

$y = \frac{11}{10} + \frac{3 x}{2}$

$\frac{3 k x}{2} + \frac{11 k}{10} + 12 x = 5$

$y = \frac{11}{10} + \frac{3 x}{2}$

Step 3

Simplify the right side.

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Step 3.1

Reorder $\frac{11}{10}$ and $\frac{3 x}{2}$ .

$y = \frac{3 x}{2} + \frac{11}{10}$

$\frac{3 k x}{2} + \frac{11 k}{10} + 12 x = 5$

$y = \frac{3 x}{2} + \frac{11}{10}$

$\frac{3 k x}{2} + \frac{11 k}{10} + 12 x = 5$