.

Since the matrices are equal, the corresponding elements are equal.

Write two linear equations.

3x + 2 = 23

– 4y – 1 = 15

First consider the equation 1.

Apply subtraction property of equality: if , then .

3x + 2 – 2 = 23 – 2          (Subtract 2 from each side)

3x = 23 – 2                       (Apply additive inverse property: 2 – 2 = 0)

3x = 21                             (Subtract: 23 – 2 = 21)

Apply division property of equality; if , then .

                       (Divided each side by 3)

                            (Cancel common terms)

x = 7                                 (Divide: )

Next consider the second equation.

Apply addition property of equality:  if , then .

– 4y – 1 = 15                (Add 1 to each side)

– 4y – 1 + 1 = 15 + 1   (Apply additive inverse property: – 1 + 1 = 0)

– 4y = 16                      (Add: 15 + 1 = 16)

Apply division property of equality; if , then .

                (Divided each side by negative 4)

                     (Cancel common terms)

y = – 4                          (Divide: )

The solution is (7, – 4).