Linear Algebra Examples

$[\begin{array}{c} 7 x \\ 12 \end{array}] = [\begin{array}{c} 28 \\ - 6 y \end{array}]$

Step 1

Write as a linear system of equations.

$7 x = 28$

$12 = - 6 y$

Step 2

Solve the system of equations.

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Step 2.1

Divide each term in $7 x = 28$ by $7$ and simplify.

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Step 2.1.1

Divide each term in $7 x = 28$ by $7$ .

$\frac{7 x}{7} = \frac{28}{7}$

$12 = - 6 y$

Step 2.1.2

Simplify the left side.

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Step 2.1.2.1

Cancel the common factor of $7$ .

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Step 2.1.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{28}{7}$

$12 = - 6 y$

Step 2.1.2.1.2

Divide $x$ by $1$ .

$x = \frac{28}{7}$

$12 = - 6 y$

$x = \frac{28}{7}$

$12 = - 6 y$

$x = \frac{28}{7}$

$12 = - 6 y$

Step 2.1.3

Simplify the right side.

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Step 2.1.3.1

Divide $28$ by $7$ .

$x = 4$

$12 = - 6 y$

$x = 4$

$12 = - 6 y$

$x = 4$

$12 = - 6 y$

Step 2.2

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

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Step 2.2.1

Rewrite the equation as $- 6 y = 12$ .

$- 6 y = 12$

$x = 4$

Step 2.2.2

Divide each term in $- 6 y = 12$ by $- 6$ and simplify.

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Step 2.2.2.1

Divide each term in $- 6 y = 12$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{12}{- 6}$

$x = 4$

Step 2.2.2.2

Simplify the left side.

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Step 2.2.2.2.1

Cancel the common factor of $- 6$ .

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Step 2.2.2.2.1.1

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{12}{- 6}$

$x = 4$

Step 2.2.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{12}{- 6}$

$x = 4$

$y = \frac{12}{- 6}$

$x = 4$

$y = \frac{12}{- 6}$

$x = 4$

Step 2.2.2.3

Simplify the right side.

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Step 2.2.2.3.1

Divide $12$ by $- 6$ .

$y = - 2$

$x = 4$

$y = - 2$

$x = 4$

$y = - 2$

$x = 4$

$y = - 2$

$x = 4$

Step 2.3

List all of the solutions.

$y = - 2, x = 4$