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

8 and - 2

Explanation:

let x be the larger number and y the smaller , then

x = 5y + 18 → (1)

3x + 4y = 16 → (2)

substitute x = 5y + 18 into (2)

3(5y + 18) + 4y = 16 ← distribute parenthesis and simplify left side

15y + 54 + 4y = 16

19y + 54 = 16 ( subtract 54 from both sides )

19y = - 38 ( divide both sides by - 19 )

y = - 2

substitute y = - 2 into (1)

x = 5(- 2) + 18 = - 10 + 18 = 8

then larger number is 8 and smaller is - 2