A system of equations is given aх – by = -24, ax + by = 4. A pair of numbers (1; -2) is its solution.

A system of equations is given aх – by = -24, ax + by = 4. A pair of numbers (1; -2) is its solution. Find the values of a and b.

A pair of numbers is equal to (1; – 2), that is, the value x = 1, y = – 2.

Substituting these values into both equations, we get a system of equations.

a * 1 – b * (- 2) = – 24, that is, a + 2b = – 24

a * 1 + b * (- 2) = 4, that is, a – 2b = 4

We solve the resulting system. Let us express a from the second equation and substitute it into the first.

a = 4 + 2b

4 + 2v + 2v = – 24

4 + 4v = – 24

4v = – 24 – 4

4v = – 28

h = – 7

we expressed the variable a through b: a = 4 + 2b = 4 + 2 * (- 7) = 4 – 14 = – 10

Answer: a = – 10, b = – 7