Question

One number is seven less than a second number. Five times the first is 2 more than 6 times the second. Find the numbers. The value of the first number is _____.

Answer 1

The system of linear equations is solved by defining two variables, substituting one into the other, and solving for the first number, which is -44.

Step-by-step explanation:

The student's question involves setting up and solving a system of linear equations to find two numbers. The conditions given are that one number is seven less than the second number, and five times the first is 2 more than six times the second.

Let's define the second number as x and the first number as y. According to the first condition, y = x - 7. The second condition can be written as the equation 5y = 6x + 2.

Now, we can replace y in the second equation with x - 7 (from the first condition) and solve for x:

• 5(x - 7) = 6x + 2
• 5x - 35 = 6x + 2
• -x = 37
• x = -37

By substituting x = -37 into the first condition, y can now be calculated:

• y = x - 7
• y = -37 - 7
• y = -44

Therefore, the first number is -44 and the second number is -37.

Answer 2

`\Large \boxed{\sf \ \ 40 \ \ }`

Step-by-step explanation:

Hello,

Let's not a and b the two numbers.

One number is seven less than a second number.

(1) b = a - 7

Five times the first is 2 more than 6 times the second.

(2) 5a = 2 + 6b

(2)+5*(1) gives

5a + 5b = 2 + 6b + 5a - 35

b = 35 - 2 = 33

a = 40

The value of the first number is
`\large \boxed{\sf \ \ 40 \ \ }`

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