Finite Math Examples

$- x - 2 y = 12$ , $2 x + 4 y = - 24$

Step 1

Represent the system of equations in matrix format.

$[\begin{array}{c} - 1 & - 2 \\ 2 & 4 \end{array}] [\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} 12 \\ - 24 \end{array}]$

Step 2

Find the determinant of the coefficient matrix $[\begin{array}{c} - 1 & - 2 \\ 2 & 4 \end{array}]$ .

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Step 2.1

Write $[\begin{array}{c} - 1 & - 2 \\ 2 & 4 \end{array}]$ in determinant notation.

$| \begin{array}{c} - 1 & - 2 \\ 2 & 4 \end{array} |$

Step 2.2

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$- 1 \cdot 4 - 2 \cdot - 2$

Step 2.3

Simplify the determinant.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Multiply $- 1$ by $4$ .

$- 4 - 2 \cdot - 2$

Step 2.3.1.2

Multiply $- 2$ by $- 2$ .

$- 4 + 4$

Step 2.3.2

Add $- 4$ and $4$ .

$0$

$D = 0$

Step 3

Since the determinant is $0$ , the system cannot be solved using Cramer's Rule.