Algebra Examples

$[\begin{array}{c} 15 \\ 7 \end{array}] - [\begin{array}{c} 6 \\ 2 \end{array}] = [\begin{array}{c} 9 \\ x \end{array}]$

Step 1

Subtract the corresponding elements.

$[\begin{array}{c} 15 - 6 \\ 7 - 2 \end{array}] = [\begin{array}{c} 9 \\ x \end{array}]$

Step 2

Simplify each element.

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Step 2.1

Subtract $6$ from $15$ .

$[\begin{array}{c} 9 \\ 7 - 2 \end{array}] = [\begin{array}{c} 9 \\ x \end{array}]$

Step 2.2

Subtract $2$ from $7$ .

$[\begin{array}{c} 9 \\ 5 \end{array}] = [\begin{array}{c} 9 \\ x \end{array}]$

Step 3

Write as a linear system of equations.

$9 = 9$

$5 = x$

Step 4

Since $9 = 9$ is always true, the matrix equation has infinite solutions.

Infinite solutions satisfying $5 = x$ .