Solve the Matrix Equation [[4a+2],[b+6]]=[[18],[6]]

$[\begin{array}{c} 4 a + 2 \\ b + 6 \end{array}] = [\begin{array}{c} 18 \\ 6 \end{array}]$

Step 1

Write as a linear system of equations.

$4 a + 2 = 18 b + 6 = 6$

Step 2

Solve the system of equations.

Solve for $a$ in $4 a + 2 = 18$ .

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

Subtract $2$ from both sides of the equation.

$4 a = 18 - 2$

$b + 6 = 6$

Subtract $2$ from $18$ .

$4 a = 16$

$b + 6 = 6$

$4 a = 16$

$b + 6 = 6$

Divide each term in $4 a = 16$ by $4$ and simplify.

Divide each term in $4 a = 16$ by $4$ .

$\frac{4 a}{4} = \frac{16}{4}$

$b + 6 = 6$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 a}{4} = \frac{16}{4}$

$b + 6 = 6$

Divide $a$ by $1$ .

$a = \frac{16}{4}$

$b + 6 = 6$

$a = \frac{16}{4}$

$b + 6 = 6$

$a = \frac{16}{4}$

$b + 6 = 6$

Simplify the right side.

Divide $16$ by $4$ .

$a = 4$

$b + 6 = 6$

$a = 4$

$b + 6 = 6$

$a = 4$

$b + 6 = 6$

$a = 4$

$b + 6 = 6$

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

Subtract $6$ from both sides of the equation.

$b = 6 - 6$

$a = 4$

Subtract $6$ from $6$ .

$b = 0$

$a = 4$

$b = 0$

$a = 4$

List all of the solutions.

$b = 0, a = 4$

Solve the Matrix Equation [[4a+2],[b+6]]=[[18],[6]]

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