Finite Math Examples

$[\begin{array}{c} 4 & - 2 \\ - 3 & 0 \end{array}] + [\begin{array}{c} w & x \\ y & z \end{array}] = [\begin{array}{c} 2 & - 3 \\ 0 & 5 \end{array}]$

Step 1

Add the corresponding elements.

$[\begin{array}{c} 4 + w & - 2 + x \\ - 3 + y & 0 + z \end{array}] = [\begin{array}{c} 2 & - 3 \\ 0 & 5 \end{array}]$

Step 2

Add $0$ and $z$ .

$[\begin{array}{c} 4 + w & - 2 + x \\ - 3 + y & z \end{array}] = [\begin{array}{c} 2 & - 3 \\ 0 & 5 \end{array}]$

Step 3

Write as a linear system of equations.

$4 + w = 2$

$- 2 + x = - 3$

$- 3 + y = 0$

$z = 5$

Step 4

Solve the system of equations.

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Step 4.1

Move all terms not containing $w$ to the right side of the equation.

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Step 4.1.1

Subtract $4$ from both sides of the equation.

$w = 2 - 4$

$- 2 + x = - 3$

$- 3 + y = 0$

$z = 5$

Step 4.1.2

Subtract $4$ from $2$ .

$w = - 2$

$- 2 + x = - 3$

$- 3 + y = 0$

$z = 5$

$w = - 2$

$- 2 + x = - 3$

$- 3 + y = 0$

$z = 5$

Step 4.2

Replace all occurrences of $w$ with $- 2$ in each equation.

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Step 4.2.1

Move all terms not containing $x$ to the right side of the equation.

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Step 4.2.1.1

Add $2$ to both sides of the equation.

$x = - 3 + 2$

$w = - 2$

$- 3 + y = 0$

$z = 5$

Step 4.2.1.2

Add $- 3$ and $2$ .

$x = - 1$

$w = - 2$

$- 3 + y = 0$

$z = 5$

$x = - 1$

$w = - 2$

$- 3 + y = 0$

$z = 5$

Step 4.2.2

Add $3$ to both sides of the equation.

$y = 3$

$x = - 1$

$w = - 2$

$z = 5$

$y = 3$

$x = - 1$

$w = - 2$

$z = 5$

Step 4.3

List all of the solutions.

$y = 3, x = - 1, w = - 2, z = 5$