Linear Algebra Examples

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

Step 1

Subtract $y$ from both sides of the equation.

$x = 4 - y$

$x - y = 2$

Step 2

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

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Step 2.1

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

$(4 - y) - y = 2$

$x = 4 - y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Subtract $y$ from $- y$ .

$4 - 2 y = 2$

$x = 4 - y$

$4 - 2 y = 2$

$x = 4 - y$

$4 - 2 y = 2$

$x = 4 - y$

Step 3

Solve for $y$ in $4 - 2 y = 2$ .

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Step 3.1

Move all terms not containing $y$ to the right side of the equation.

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Step 3.1.1

Subtract $4$ from both sides of the equation.

$- 2 y = 2 - 4$

$x = 4 - y$

Step 3.1.2

Subtract $4$ from $2$ .

$- 2 y = - 2$

$x = 4 - y$

$- 2 y = - 2$

$x = 4 - y$

Step 3.2

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

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Step 3.2.1

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

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

$x = 4 - y$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.2.1.1

Cancel the common factor.

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

$x = 4 - y$

Step 3.2.2.1.2

Divide $y$ by $1$ .

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

$x = 4 - y$

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

$x = 4 - y$

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

$x = 4 - y$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $- 2$ by $- 2$ .

$y = 1$

$x = 4 - y$

$y = 1$

$x = 4 - y$

$y = 1$

$x = 4 - y$

$y = 1$

$x = 4 - y$

Step 4

Replace all occurrences of $y$ with $1$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = 4 - y$ with $1$ .

$x = 4 - (1)$

$y = 1$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $4 - (1)$ .

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Step 4.2.1.1

Multiply $- 1$ by $1$ .

$x = 4 - 1$

$y = 1$

Step 4.2.1.2

Subtract $1$ from $4$ .

$x = 3$

$y = 1$

$x = 3$

$y = 1$

$x = 3$

$y = 1$

$x = 3$

$y = 1$

Step 5

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

$(3, 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(3, 1)$

Equation Form:

$x = 3, y = 1$

Step 7

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