Algebra Examples

$y = 2 x - 1$ $2 x - y - 1 = 0$

Step 1

Replace all occurrences of $y$ with $2 x - 1$ in each equation.

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Step 1.1

Replace all occurrences of $y$ in $2 x - y - 1 = 0$ with $2 x - 1$ .

$2 x - (2 x - 1) - 1 = 0$

$y = 2 x - 1$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $2 x - (2 x - 1) - 1$ .

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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.

$2 x - (2 x) + 1 - 1 = 0$

$y = 2 x - 1$

Step 1.2.1.1.2

Multiply $2$ by $- 1$ .

$2 x - 2 x + 1 - 1 = 0$

$y = 2 x - 1$

Step 1.2.1.1.3

Multiply $- 1$ by $- 1$ .

$2 x - 2 x + 1 - 1 = 0$

$y = 2 x - 1$

$2 x - 2 x + 1 - 1 = 0$

$y = 2 x - 1$

Step 1.2.1.2

Combine the opposite terms in $2 x - 2 x + 1 - 1$ .

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Step 1.2.1.2.1

Subtract $2 x$ from $2 x$ .

$0 + 1 - 1 = 0$

$y = 2 x - 1$

Step 1.2.1.2.2

Subtract $1$ from $1$ .

$0 + 0 = 0$

$y = 2 x - 1$

Step 1.2.1.2.3

Add $0$ and $0$ .

$0 = 0$

$y = 2 x - 1$

$0 = 0$

$y = 2 x - 1$

$0 = 0$

$y = 2 x - 1$

$0 = 0$

$y = 2 x - 1$

$0 = 0$

$y = 2 x - 1$

Step 2

Remove any equations from the system that are always true.

$y = 2 x - 1$

Step 3