Finite Math Examples

$- 2 x [\begin{array}{c} 2 & - 8 \\ - 4 & 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Step 1

Multiply $- 2 x$ by each element of the matrix.

$[\begin{array}{c} - 2 x \cdot 2 & - 2 x \cdot - 8 \\ - 2 x \cdot - 4 & - 2 x \cdot 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Step 2

Simplify each element in the matrix.

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Step 2.1

Multiply $2$ by $- 2$ .

$[\begin{array}{c} - 4 x & - 2 x \cdot - 8 \\ - 2 x \cdot - 4 & - 2 x \cdot 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Step 2.2

Multiply $- 8$ by $- 2$ .

$[\begin{array}{c} - 4 x & 16 x \\ - 2 x \cdot - 4 & - 2 x \cdot 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Step 2.3

Multiply $- 4$ by $- 2$ .

$[\begin{array}{c} - 4 x & 16 x \\ 8 x & - 2 x \cdot 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Step 2.4

Multiply $2$ by $- 2$ .

$[\begin{array}{c} - 4 x & 16 x \\ 8 x & - 4 x \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Step 3

Write as a linear system of equations.

$- 4 x = 4$

$16 x = - 6$

$8 x = 2$

$- 4 x = - 8$

Step 4

Solve the system of equations.

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Step 4.1

Divide each term in $- 4 x = 4$ by $- 4$ and simplify.

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Step 4.1.1

Divide each term in $- 4 x = 4$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{4}{- 4}$

$16 x = - 6$

$8 x = 2$

$- 4 x = - 8$

Step 4.1.2

Simplify the left side.

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Step 4.1.2.1

Cancel the common factor of $- 4$ .

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Step 4.1.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{4}{- 4}$

$16 x = - 6$

$8 x = 2$

$- 4 x = - 8$

Step 4.1.2.1.2

Divide $x$ by $1$ .

$x = \frac{4}{- 4}$

$16 x = - 6$

$8 x = 2$

$- 4 x = - 8$

$x = \frac{4}{- 4}$

$16 x = - 6$

$8 x = 2$

$- 4 x = - 8$

$x = \frac{4}{- 4}$

$16 x = - 6$

$8 x = 2$

$- 4 x = - 8$

Step 4.1.3

Simplify the right side.

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Step 4.1.3.1

Divide $4$ by $- 4$ .

$x = - 1$

$16 x = - 6$

$8 x = 2$

$- 4 x = - 8$

$x = - 1$

$16 x = - 6$

$8 x = 2$

$- 4 x = - 8$

$x = - 1$

$16 x = - 6$

$8 x = 2$

$- 4 x = - 8$

Step 4.2

Replace all occurrences of $x$ with $- 1$ in each equation.

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Step 4.2.1

Replace all occurrences of $x$ in $16 x = - 6$ with $- 1$ .

$16 (- 1) = - 6$

$x = - 1$

$8 x = 2$

$- 4 x = - 8$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Multiply $16$ by $- 1$ .

$- 16 = - 6$

$x = - 1$

$8 x = 2$

$- 4 x = - 8$

$- 16 = - 6$

$x = - 1$

$8 x = 2$

$- 4 x = - 8$

Step 4.2.3

Replace all occurrences of $x$ in $8 x = 2$ with $- 1$ .

$8 (- 1) = 2$

$- 16 = - 6$

$x = - 1$

$- 4 x = - 8$

Step 4.2.4

Simplify the left side.

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Step 4.2.4.1

Multiply $8$ by $- 1$ .

$- 8 = 2$

$- 16 = - 6$

$x = - 1$

$- 4 x = - 8$

$- 8 = 2$

$- 16 = - 6$

$x = - 1$

$- 4 x = - 8$

Step 4.2.5

Replace all occurrences of $x$ in $- 4 x = - 8$ with $- 1$ .

$- 4 \cdot - 1 = - 8$

$- 8 = 2$

$- 16 = - 6$

$x = - 1$

Step 4.2.6

Simplify the left side.

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Step 4.2.6.1

Multiply $- 4$ by $- 1$ .

$4 = - 8$

$- 8 = 2$

$- 16 = - 6$

$x = - 1$

$4 = - 8$

$- 8 = 2$

$- 16 = - 6$

$x = - 1$

$4 = - 8$

$- 8 = 2$

$- 16 = - 6$

$x = - 1$

Step 4.3

Since $4 = - 8$ is not true, there is no solution.

$No solution$