Linear Algebra Examples

$y = 3 x$ , $4 x - 3 y = 20$

Step 1

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

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Step 1.1

Replace all occurrences of $y$ in $4 x - 3 y = 20$ with $3 x$ .

$4 x - 3 (3 x) = 20$

$y = 3 x$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $4 x - 3 (3 x)$ .

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Step 1.2.1.1

Multiply $3$ by $- 3$ .

$4 x - 9 x = 20$

$y = 3 x$

Step 1.2.1.2

Subtract $9 x$ from $4 x$ .

$- 5 x = 20$

$y = 3 x$

$- 5 x = 20$

$y = 3 x$

$- 5 x = 20$

$y = 3 x$

$- 5 x = 20$

$y = 3 x$

Step 2

Divide each term in $- 5 x = 20$ by $- 5$ and simplify.

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Step 2.1

Divide each term in $- 5 x = 20$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{20}{- 5}$

$y = 3 x$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{20}{- 5}$

$y = 3 x$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{20}{- 5}$

$y = 3 x$

$x = \frac{20}{- 5}$

$y = 3 x$

$x = \frac{20}{- 5}$

$y = 3 x$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $20$ by $- 5$ .

$x = - 4$

$y = 3 x$

$x = - 4$

$y = 3 x$

$x = - 4$

$y = 3 x$

Step 3

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

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Step 3.1

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

$y = 3 (- 4)$

$x = - 4$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $3$ by $- 4$ .

$y = - 12$

$x = - 4$

$y = - 12$

$x = - 4$

$y = - 12$

$x = - 4$

Step 4

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

$(- 4, - 12)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 4, - 12)$

Equation Form:

$x = - 4, y = - 12$

Step 6