Calculus Examples

$2 x + y = 2$ , $4 x + 2 y = 4$

Step 1

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

$y = 2 - 2 x$

$4 x + 2 y = 4$

Step 2

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

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Step 2.1

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

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

$y = 2 - 2 x$

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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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.

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

$y = 2 - 2 x$

Step 2.2.1.1.2

Multiply $2$ by $2$ .

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

$y = 2 - 2 x$

Step 2.2.1.1.3

Multiply $- 2$ by $2$ .

$4 x + 4 - 4 x = 4$

$y = 2 - 2 x$

$4 x + 4 - 4 x = 4$

$y = 2 - 2 x$

Step 2.2.1.2

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

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Step 2.2.1.2.1

Subtract $4 x$ from $4 x$ .

$0 + 4 = 4$

$y = 2 - 2 x$

Step 2.2.1.2.2

Add $0$ and $4$ .

$4 = 4$

$y = 2 - 2 x$

$4 = 4$

$y = 2 - 2 x$

$4 = 4$

$y = 2 - 2 x$

$4 = 4$

$y = 2 - 2 x$

$4 = 4$

$y = 2 - 2 x$

Step 3

Remove any equations from the system that are always true.

$y = 2 - 2 x$

Step 4