The equation is .

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

Write two linear equations.

x + 3y = –22

2x – y = 19

Consider the second equation

2x – y = 19

Apply addition property of equality: If , then .

2x – y + y = 19 + y             (Add y to each side) \ \

2x = 19 + y                         (Apply additive inverse property: – y + y = 0)

Apply division property of equality: if , then .

                   (Divide each side by 2) \ \

                        (Cancel common terms) \ \

Substitute in x + 3y = – 22.

          (Simplify)

Apply multiplication property of equality: if , then .

            (Multiply each side by 2)

                   (Cancel common terms)

19 + y + 6y = – 44                       (Multiply: )

19 + 7y = – 44                             (Add: 6y + y = 7y)

Apply subtraction property of equality: if , then .

19 – 19 + 7y = – 44 – 19       (Subtraction 19 from each side)

19 – 19 + 7y = – 44 – 19       (Apply additive inverse property: 19 – 19 = 0)

7y = – 63                                (Subtract: – 44 – 19 = – 63)

Apply division property of equality; if , then .

                           (Divide each side by 7)

                                (Cancel common terms)

y = – 9                                     (Multiply: )

To find the value of x, substitute – 9 for y in second equation.

2x + 9 = 19                          (Product of two same signs is positive)

2x + 9 – 9 = 19 – 9             (Subtract 9 from each side)

2x = 19 – 9                          (Apply additive inverse property: 9 – 9 = 0)

2x = 10                                (Subtract: 19 – 9 = 10)

Apply division property of equality; if , then .

                          (Divide each side by 2)

                              (Cancel common terms)

x = 5                                   (Divide: )

The solution is (5, – 9).