An algebraic expression of the form $a + bx$ has the value of $15$ when $x = 2$ and the value of $3$ when $x = 5$. Calculate $a + b$.
a + b (2) = 15
a + b (5) = 3 subtract the second equation from the first and we have
-3b = 12 divide both sides by -3
b = -4
Sub this into the first equation and we have
a + -4(2) = 15
a - 8 = 15 add 8 to both sides
a = 23
So a + b = 23 + (-4) = 19
