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)
[tex]a(3(0)-8)=b-18(0)\\a(-8)=b\\b=-8a[/tex]
For 1 (Equation #2)
[tex]a(3(1)-8)=b-18(1)\\a(-5)=b-18\\-5a+18=b\\b=18-5a[/tex]
We can solve the system by replacing equation #1 in equation #2 like this:
[tex]-8a=18-5a\\-8a+5a=18\\-3a=18\\a=\frac{18}{-3} \\a=-6[/tex]
Now we can replace the value of a in equation #1
[tex]b=-8(-6)\\b=48[/tex]
