The pair of numbers (-2; 3) is the solution of the equations {3x-by + 4b = -1 {ax + 2y + a + b = 19

The pair of numbers (-2; 3) is the solution of the equations {3x-by + 4b = -1 {ax + 2y + a + b = 19 find the values of a and b.

1. A given pair of numbers must satisfy both equations of the system:

{3x – by + 4b = -1;
{ax + 2y + a + b = 19;

x = -2; y = 3;

{3 * (-2) – b * 3 + 4b = -1;
{a * (-2) + 2 * 3 + a + b = 19.

2. Let’s solve the system of two equations for the variables a and b:

{-6 – 3b + 4b = -1;
{-2a + 6 + a + b = 19;
{b = 6 – 1;
{b – a = 19 – 6;
{b = 5;
{5 – a = 13;
{b = 5;
{a = 5 – 13;
{b = 5;
{a = -8.
Answer: a = -8; b = 5.