Question

Let x represent one number, and y represent another number. The word problem can be represented by the following linear equation:

x = 4y - 3
The sum of these two numbers is 47, so you can also write:
x + y = 47

Answer 1

The solution to the system of linear equations x = 4y - 3 and x + y = 47 reveals that the two numbers are 37 and 10, which add up to 47.

Step-by-step explanation:

The question provided is concerned with linear equations and their solutions within a system of equations. The first equation, x = 4y - 3, shows a direct relationship between x and y where x is expressed in terms of y. The second equation, x + y = 47, indicates that the sum of both variables equals 47. To solve for both x and y, we can substitute the expression for x from the first equation into the second, yielding 4y - 3 + y = 47. Combining like terms results in 5y - 3 = 47, and solving for y gives us y = 10. Substituting this value back into the first equation, we find that x = 4(10) - 3 = 40 - 3 = 37. Finally, verifying our solution, we add them together to ensure that 37 + 10 = 47, which is true. Therefore, the numbers represented by x and y are 37 and 10, respectively.