Find the two numbers. Solve using algebra

Question

The larger of two negative numbers is five more than the smaller number. If twice the smaller number is increased by 28, the result is the larger number multiplied by -7. Find the two numbers. Solve using algebra.

Answer 1

Michelle, we can solve this using substitution in a system of equations.

 

Let's let s = the smaller number and l = the larger. In this case, we have l = s + 5.

 

We also have 2s + 28 = -7l

 

Since the first equation is already solved for l, we can substitute the "value" of l into the 2nd equation.

 

2s + 28 = -7(s + 5)

2s + 28 = -7s -35

         9s = -63

           s = -7

 

So, l = -2

 

Let's check. 2(-7) + 28 =-2(-7)

                          -14 + 28 = 14

                                    14 = 14

 

Check!

 

Hope this helps!