Linear Algebra Examples

$- x + 3 y - 3 = 0$ , $x - 3 y = 3$

Step 1

Add $3 y$ to both sides of the equation.

$x = 3 + 3 y$

$- x + 3 y - 3 = 0$

Step 2

Replace all occurrences of $x$ with $3 + 3 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- x + 3 y - 3 = 0$ with $3 + 3 y$ .

$- (3 + 3 y) + 3 y - 3 = 0$

$x = 3 + 3 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- (3 + 3 y) + 3 y - 3$ .

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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.

$- 1 \cdot 3 - (3 y) + 3 y - 3 = 0$

$x = 3 + 3 y$

Step 2.2.1.1.2

Multiply $- 1$ by $3$ .

$- 3 - (3 y) + 3 y - 3 = 0$

$x = 3 + 3 y$

Step 2.2.1.1.3

Multiply $3$ by $- 1$ .

$- 3 - 3 y + 3 y - 3 = 0$

$x = 3 + 3 y$

$- 3 - 3 y + 3 y - 3 = 0$

$x = 3 + 3 y$

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Combine the opposite terms in $- 3 - 3 y + 3 y - 3$ .

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Step 2.2.1.2.1.1

Add $- 3 y$ and $3 y$ .

$- 3 + 0 - 3 = 0$

$x = 3 + 3 y$

Step 2.2.1.2.1.2

Add $- 3$ and $0$ .

$- 3 - 3 = 0$

$x = 3 + 3 y$

$- 3 - 3 = 0$

$x = 3 + 3 y$

Step 2.2.1.2.2

Subtract $3$ from $- 3$ .

$- 6 = 0$

$x = 3 + 3 y$

$- 6 = 0$

$x = 3 + 3 y$

$- 6 = 0$

$x = 3 + 3 y$

$- 6 = 0$

$x = 3 + 3 y$

$- 6 = 0$

$x = 3 + 3 y$

Step 3

Since $- 6 = 0$ is not true, there is no solution.

No solution

Step 4