Question

18. One number is 3 less than a second number. Twice the second number is 12 more than 3 times the first.

Answer 1

Answer: The numbers are -3 and - 6

Step-by-step explanation:

Let the first number be x and the second number be y , then from the first statement we have

x + 3 = y  ............. equation 1

From the second statement

2y  = 3x + 12 ............ equation 2

solving the resulting simultaneous equation by substitution method ,we have:

substitute x - 3= y  into equation 2 , we have

2( x + 3) = 3x + 12

2x + 6 = 3x +  12

2x - 3x = 6

x = -6

substitute x = - 6 into equation 1 , that is

- 6 + 3 = y

Therefore ,

y = -3

2y = 3y + 3

Check:

x + 3 = y , implies

-6 + 3 = -3 = y

Also 2y = 3x + 12 , implies

2(-3) = -6

3(-6) + 12 = -6