Precalculus Examples

$x = 7 y - 1$ , $- 3 x + 21 y = 3$

Step 1

Replace all occurrences of $x$ with $7 y - 1$ in each equation.

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Step 1.1

Replace all occurrences of $x$ in $- 3 x + 21 y = 3$ with $7 y - 1$ .

$- 3 (7 y - 1) + 21 y = 3$

$x = 7 y - 1$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $- 3 (7 y - 1) + 21 y$ .

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Step 1.2.1.1

Simplify each term.

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Step 1.2.1.1.1

Apply the distributive property.

$- 3 (7 y) - 3 \cdot - 1 + 21 y = 3$

$x = 7 y - 1$

Step 1.2.1.1.2

Multiply $7$ by $- 3$ .

$- 21 y - 3 \cdot - 1 + 21 y = 3$

$x = 7 y - 1$

Step 1.2.1.1.3

Multiply $- 3$ by $- 1$ .

$- 21 y + 3 + 21 y = 3$

$x = 7 y - 1$

$- 21 y + 3 + 21 y = 3$

$x = 7 y - 1$

Step 1.2.1.2

Combine the opposite terms in $- 21 y + 3 + 21 y$ .

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Step 1.2.1.2.1

Add $- 21 y$ and $21 y$ .

$0 + 3 = 3$

$x = 7 y - 1$

Step 1.2.1.2.2

Add $0$ and $3$ .

$3 = 3$

$x = 7 y - 1$

$3 = 3$

$x = 7 y - 1$

$3 = 3$

$x = 7 y - 1$

$3 = 3$

$x = 7 y - 1$

$3 = 3$

$x = 7 y - 1$

Step 2

Remove any equations from the system that are always true.

$x = 7 y - 1$

Step 3