Algebra Examples

$2 x + y = 4$ $- 4 x - 2 y = - 8$

Step 1

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

$y = 4 - 2 x$

$- 4 x - 2 y = - 8$

Step 2

Replace all occurrences of $y$ with $4 - 2 x$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $- 4 x - 2 y = - 8$ with $4 - 2 x$ .

$- 4 x - 2 (4 - 2 x) = - 8$

$y = 4 - 2 x$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 4 x - 2 (4 - 2 x)$ .

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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.

$- 4 x - 2 \cdot 4 - 2 (- 2 x) = - 8$

$y = 4 - 2 x$

Step 2.2.1.1.2

Multiply $- 2$ by $4$ .

$- 4 x - 8 - 2 (- 2 x) = - 8$

$y = 4 - 2 x$

Step 2.2.1.1.3

Multiply $- 2$ by $- 2$ .

$- 4 x - 8 + 4 x = - 8$

$y = 4 - 2 x$

$- 4 x - 8 + 4 x = - 8$

$y = 4 - 2 x$

Step 2.2.1.2

Combine the opposite terms in $- 4 x - 8 + 4 x$ .

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Step 2.2.1.2.1

Add $- 4 x$ and $4 x$ .

$0 - 8 = - 8$

$y = 4 - 2 x$

Step 2.2.1.2.2

Subtract $8$ from $0$ .

$- 8 = - 8$

$y = 4 - 2 x$

$- 8 = - 8$

$y = 4 - 2 x$

$- 8 = - 8$

$y = 4 - 2 x$

$- 8 = - 8$

$y = 4 - 2 x$

$- 8 = - 8$

$y = 4 - 2 x$

Step 3

Remove any equations from the system that are always true.

$y = 4 - 2 x$

Step 4