Question: One number is one less than a second number. Twice the first is 4 more than 5 times the second. Find the numbers.
Answer:
The numbers are -3 and -2
Step-by-step explanation:
Given
Let the numbers be a and b
From the first statement:
[tex]a = b - 1[/tex]
From the second:
[tex]2a = 4 + 5b[/tex]
Required
Find a and b
Substitute b - 1 for a in the second equation
[tex]2(b-1) = 4 + 5b[/tex]
[tex]2b-2 = 4 + 5b[/tex]
Collect like terms
[tex]2b- 5b = 2+ 4[/tex]
[tex]-3b = 6[/tex]
[tex]b =-2[/tex]
Recall that:
[tex]a = b - 1[/tex]
[tex]a = -2 - 1[/tex]
[tex]a =- 3[/tex]
