Linear Algebra Examples

$x + 2 y = 4$ , $2 x + 4 y = 32$

Step 1

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

$x = 4 - 2 y$

$2 x + 4 y = 32$

Step 2

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

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Step 2.1

Replace all occurrences of $x$ in $2 x + 4 y = 32$ with $4 - 2 y$ .

$2 (4 - 2 y) + 4 y = 32$

$x = 4 - 2 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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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.

$2 \cdot 4 + 2 (- 2 y) + 4 y = 32$

$x = 4 - 2 y$

Step 2.2.1.1.2

Multiply $2$ by $4$ .

$8 + 2 (- 2 y) + 4 y = 32$

$x = 4 - 2 y$

Step 2.2.1.1.3

Multiply $- 2$ by $2$ .

$8 - 4 y + 4 y = 32$

$x = 4 - 2 y$

$8 - 4 y + 4 y = 32$

$x = 4 - 2 y$

Step 2.2.1.2

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

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Step 2.2.1.2.1

Add $- 4 y$ and $4 y$ .

$8 + 0 = 32$

$x = 4 - 2 y$

Step 2.2.1.2.2

Add $8$ and $0$ .

$8 = 32$

$x = 4 - 2 y$

$8 = 32$

$x = 4 - 2 y$

$8 = 32$

$x = 4 - 2 y$

$8 = 32$

$x = 4 - 2 y$

$8 = 32$

$x = 4 - 2 y$

Step 3

Since $8 = 32$ is not true, there is no solution.

No solution

Step 4