Question

In the following equation, a and b are both integers. a(3x-8)=b -18x

what is the value of a ?

what is the value of b?

Answer 1

The value of a is -6
The value of b is 48

Answer 2

If a and b are two fixed integers this means the equations is a straight line where x values could be any number within (-∞,∞). So we can evaluate any two numbers to obtain a set of two different equations to solve the system for a and b. The number we will try are 0 and 1:

For 0 (Equation #1)

$a(3(0)-8)=b-18(0)\\a(-8)=b\\b=-8a$

For 1 (Equation #2)

$a(3(1)-8)=b-18(1)\\a(-5)=b-18\\-5a+18=b\\b=18-5a$

We can solve the system by replacing equation #1 in equation #2 like this:

$-8a=18-5a\\-8a+5a=18\\-3a=18\\a=\frac{18}{-3} \\a=-6$

Now we can replace the value of a in equation #1

$b=-8(-6)\\b=48$