Precalculus Examples

$[\begin{array}{c} 5 & - 3 x \\ y & - 6 \end{array}] = [\begin{array}{c} 5 & 18 \\ - 4 & - 6 \end{array}]$

Step 1

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

$5 = 5$

$- 3 x = 18$

$y = - 4$

$- 6 = - 6$

Step 2

Divide each term in $- 3 x = 18$ by $- 3$ and simplify.

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Step 2.1

Divide each term in $- 3 x = 18$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{18}{- 3}$

$y = - 4$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{18}{- 3}$

$y = - 4$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{18}{- 3}$

$y = - 4$

$x = \frac{18}{- 3}$

$y = - 4$

$x = \frac{18}{- 3}$

$y = - 4$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $18$ by $- 3$ .

$x = - 6$

$y = - 4$

$x = - 6$

$y = - 4$

$x = - 6$

$y = - 4$

Step 3

Solve the system of equations.

$x = - 6 y = - 4$

Step 4

List all of the solutions.

$x = - 6, y = - 4$