Linear Algebra Examples

$[\begin{array}{c} 6 x \\ 25 \end{array}] = [\begin{array}{c} - 9 \\ 5 y \end{array}]$

Step 1

The matrix equation can be written as a set of equations.

$6 x = - 9$

$25 = 5 y$

Step 2

Divide each term in $6 x = - 9$ by $6$ and simplify.

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Step 2.1

Divide each term in $6 x = - 9$ by $6$ .

$\frac{6 x}{6} = \frac{- 9}{6}$

$25 = 5 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $6$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 9}{6}$

$25 = 5 y$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 9}{6}$

$25 = 5 y$

$x = \frac{- 9}{6}$

$25 = 5 y$

$x = \frac{- 9}{6}$

$25 = 5 y$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $- 9$ and $6$ .

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Step 2.3.1.1

Factor $3$ out of $- 9$ .

$x = \frac{3 (- 3)}{6}$

$25 = 5 y$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $3$ out of $6$ .

$x = \frac{3 \cdot - 3}{3 \cdot 2}$

$25 = 5 y$

Step 2.3.1.2.2

Cancel the common factor.

$x = \frac{3 \cdot - 3}{3 \cdot 2}$

$25 = 5 y$

Step 2.3.1.2.3

Rewrite the expression.

$x = \frac{- 3}{2}$

$25 = 5 y$

$x = \frac{- 3}{2}$

$25 = 5 y$

$x = \frac{- 3}{2}$

$25 = 5 y$

Step 2.3.2

Move the negative in front of the fraction.

$x = - \frac{3}{2}$

$25 = 5 y$

$x = - \frac{3}{2}$

$25 = 5 y$

$x = - \frac{3}{2}$

$25 = 5 y$

Step 3

Replace all occurrences of $x$ with $- \frac{3}{2}$ in each equation.

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Step 3.1

Rewrite the equation as $5 y = 25$ .

$5 y = 25$

$x = - \frac{3}{2}$

Step 3.2

Divide each term in $5 y = 25$ by $5$ and simplify.

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Step 3.2.1

Divide each term in $5 y = 25$ by $5$ .

$\frac{5 y}{5} = \frac{25}{5}$

$x = - \frac{3}{2}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $5$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{25}{5}$

$x = - \frac{3}{2}$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{25}{5}$

$x = - \frac{3}{2}$

$y = \frac{25}{5}$

$x = - \frac{3}{2}$

$y = \frac{25}{5}$

$x = - \frac{3}{2}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $25$ by $5$ .

$y = 5$

$x = - \frac{3}{2}$

$y = 5$

$x = - \frac{3}{2}$

$y = 5$

$x = - \frac{3}{2}$

$y = 5$

$x = - \frac{3}{2}$

Step 4

List all of the solutions.

$y = 5, x = - \frac{3}{2}$