You should first define your variables:
x = first integer
y = second integer
The sum of two integers is 33 translates to: x+y=33
The product of two integers is 266 translates to xy = 266
To solve this system of equations, use substitution.
Solve the first equation for y: y=33-x
Substitute 33-x for the y in the second equation: x(33-x)=266
Multiply and set the equation equal to 0: -x2 + 33x -266 = 0
From here, you can either factor, graph or use the quadratic formula to solve.
Factoring:
Divide the equation by -1: x2-33x+266=0
What multiples to 266 and adds to -33? -19 and -14
(x - 19)(x - 14) = 0
x must be 19 or 14, so y is the opposite number.
