Question

Write and solve a system of linear equations: The larger of two numbers is 18 more than 5 times the smaller. If 3 times the larger number is increased by 4 times the smaller, the result is 16. Find the numbers by solving algebraically. Show your work including the equations

Answer 1

Answer:

8 and -2

Step-by-step explanation:

Let the numbers be l and s.

We have equations:

l = 5s + 18

3l + 4s = 16

Solve for s by substituting l into the second equation:

3(5s + 18) + 4s = 16

15s + 54 + 4s = 16

19s = 16 - 54

19s = -38

s = -38/19

s = -2

Find the value of l:

l = 5(-2) + 18

l = -10 + 18

l = 8