Algebra Examples

$2 x + y = 6$ AND $3 y - 18 = - 6 x$

Step 1

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

$y = 6 - 2 x$

$3 y - 18 = - 6 x$

Step 2

Replace all occurrences of $y$ with $6 - 2 x$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $3 y - 18 = - 6 x$ with $6 - 2 x$ .

$3 (6 - 2 x) - 18 = - 6 x$

$y = 6 - 2 x$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $3 (6 - 2 x) - 18$ .

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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.

$3 \cdot 6 + 3 (- 2 x) - 18 = - 6 x$

$y = 6 - 2 x$

Step 2.2.1.1.2

Multiply $3$ by $6$ .

$18 + 3 (- 2 x) - 18 = - 6 x$

$y = 6 - 2 x$

Step 2.2.1.1.3

Multiply $- 2$ by $3$ .

$18 - 6 x - 18 = - 6 x$

$y = 6 - 2 x$

$18 - 6 x - 18 = - 6 x$

$y = 6 - 2 x$

Step 2.2.1.2

Combine the opposite terms in $18 - 6 x - 18$ .

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Step 2.2.1.2.1

Subtract $18$ from $18$ .

$- 6 x + 0 = - 6 x$

$y = 6 - 2 x$

Step 2.2.1.2.2

Add $- 6 x$ and $0$ .

$- 6 x = - 6 x$

$y = 6 - 2 x$

$- 6 x = - 6 x$

$y = 6 - 2 x$

$- 6 x = - 6 x$

$y = 6 - 2 x$

$- 6 x = - 6 x$

$y = 6 - 2 x$

$- 6 x = - 6 x$

$y = 6 - 2 x$

Step 3

Remove any equations from the system that are always true.

$y = 6 - 2 x$

Step 4