Linear Algebra Examples

$x + y = 0$ , $3 x + y = 4$

Step 1

Subtract $y$ from both sides of the equation.

$x = - y$

$3 x + y = 4$

Step 2

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

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Step 2.1

Replace all occurrences of $x$ in $3 x + y = 4$ with $- y$ .

$3 (- y) + y = 4$

$x = - y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $3 (- y) + y$ .

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Step 2.2.1.1

Multiply $- 1$ by $3$ .

$- 3 y + y = 4$

$x = - y$

Step 2.2.1.2

Add $- 3 y$ and $y$ .

$- 2 y = 4$

$x = - y$

$- 2 y = 4$

$x = - y$

$- 2 y = 4$

$x = - y$

$- 2 y = 4$

$x = - y$

Step 3

Divide each term in $- 2 y = 4$ by $- 2$ and simplify.

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Step 3.1

Divide each term in $- 2 y = 4$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{4}{- 2}$

$x = - y$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{4}{- 2}$

$x = - y$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{4}{- 2}$

$x = - y$

$y = \frac{4}{- 2}$

$x = - y$

$y = \frac{4}{- 2}$

$x = - y$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $4$ by $- 2$ .

$y = - 2$

$x = - y$

$y = - 2$

$x = - y$

$y = - 2$

$x = - y$

Step 4

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

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Step 4.1

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

$x = - (- 2)$

$y = - 2$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- 1$ by $- 2$ .

$x = 2$

$y = - 2$

$x = 2$

$y = - 2$

$x = 2$

$y = - 2$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(2, - 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(2, - 2)$

Equation Form:

$x = 2, y = - 2$

Step 7