Linear Algebra Examples

$x - y = 3$ , $2 x - y = 4$

Step 1

Add $y$ to both sides of the equation.

$x = 3 + y$

$2 x - y = 4$

Step 2

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

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Step 2.1

Replace all occurrences of $x$ in $2 x - y = 4$ with $3 + y$ .

$2 (3 + y) - y = 4$

$x = 3 + y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $2 (3 + y) - y$ .

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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.

$2 \cdot 3 + 2 y - y = 4$

$x = 3 + y$

Step 2.2.1.1.2

Multiply $2$ by $3$ .

$6 + 2 y - y = 4$

$x = 3 + y$

$6 + 2 y - y = 4$

$x = 3 + y$

Step 2.2.1.2

Subtract $y$ from $2 y$ .

$6 + y = 4$

$x = 3 + y$

$6 + y = 4$

$x = 3 + y$

$6 + y = 4$

$x = 3 + y$

$6 + y = 4$

$x = 3 + y$

Step 3

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

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Step 3.1

Subtract $6$ from both sides of the equation.

$y = 4 - 6$

$x = 3 + y$

Step 3.2

Subtract $6$ from $4$ .

$y = - 2$

$x = 3 + y$

$y = - 2$

$x = 3 + y$

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 $x = 3 + y$ with $- 2$ .

$x = 3 - 2$

$y = - 2$

Step 4.2

Simplify $x = 3 - 2$ .

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Remove parentheses.

$x = 3 - 2$

$y = - 2$

$x = 3 - 2$

$y = - 2$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Subtract $2$ from $3$ .

$x = 1$

$y = - 2$

$x = 1$

$y = - 2$

$x = 1$

$y = - 2$

$x = 1$

$y = - 2$

Step 5

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

$(1, - 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(1, - 2)$

Equation Form:

$x = 1, y = - 2$

Step 7