Solve algebraically 6a + b = 16 & 5a - 2b = 19

6a + b = 16    Equation 1
5a - 2b = 19    Equation 2

Scale up one equation so both equations have same coeffient of one variable ie 2 times Equ 1

12a + 2b = 32
5a - 2b = 19

Add variables of each equation, hence eliminating variable b

17a = 51

Divide both sides by 17

a=3

Substitute a=3 into either one of the original equations

5(3) - 2b = 19

15 - 2b = 19

Subtract 15 from both sides of equation

-2b = 4

Divide both sides by -2

b = -2

Hence final answer: a=3, b=-2