What are the coefficients a and b if it is known that a pair of numbers (-1; -2)

What are the coefficients a and b if it is known that a pair of numbers (-1; -2) is a solution to the system of equations {5 x + ay = -1 and {bx-4y = 5

To calculate the coefficients of the system of equations {5x + ay = -1, bx – 4y = 5, knowing that the pair of numbers (-1; -2) is a solution to this system, we substitute these numbers into the system and, having obtained equations with unknowns a and b , let’s solve them.

1) Finding the coefficient a through the first equation of the system:

5 * (-1) + a * (-2) = -1;

-5 – 2a = -1;

-2a = 5 – 1;

-2a = 4;

a = 4 / (-2);

a = -2.

2) Finding the coefficient b through the second equation of the system:

b * (-1) – 4 * (-2) = 5;

-b + 8 = 5;

-b = 5 – 8;

-b = -3;

b = -3 / (-1);

b = 3.

Answer: a = -2, b = 3.