Algebraic word problem

Question

Given that y = ax + b/8. When y = 1, x = 13 and when y = -1, x = -3. What is the value of b?

Answer 1

Hi Rosalita,

When y=1 and x=13, the equation becomes 1 = 13a + b/8.

When y=-1 and x=-3, the equation becomes -1 = -3a + b/8.

Since we plugged in values for x and y, the only variables left are a and b. We have two equations with two variables--that is, a system of equations where the variables are a and b.

There are several ways to solve a system of equations--the way that stands out to me is the elimination method. I will subtract the two equations from one another, because this will eliminate b:

(1 = 13a + b/8)

- (-1 = -3a + b/8)

2 = 16a

Since now there is only one variable, it is easy to solve this equation for a: a=1/8.

Now that we have the value of a, we can use either of our two original equations with a and b to find b.

1 = 13a + b/8

1 = 13(1/8) + b/8

1 = 13/8 + b/8

-5/8 = b/8

b=-5

Hope this helps,

The Mathematic Fanatic