2. The sum of two numbers is 15. The larger number is 2 less than three times

the smaller number. What are the two numbers?

Write an equation that can be used to express the problem as a system of two

linear equations in slope-intercept form.

Let the small number be X and the large number be Y.

Sum means add, so X + Y = 15

Then Y = 3X - 2

Now you have X + 3X - 2 = 15

Simplify:

4x - 2 = 15

Add 2 to both numbers

4x = 17

Divide both sides by 4:

X = 17/4 = 4 1/4

Y = 15 - 4 1/4 = 10 3/4

The numbers are 4 1/4 and 10 3/4