Question: ALDEIRA F/BEC25/PER03 (LMS) 4-2: Homework (LMS graded) Part 1 of 2 The number of men and women…

ALDEIRA F/BEC25/PER03 (LMS) 4-2: Homework (LMS graded)

Part 1 of 2

The number of men and women receiving bachelor’s degrees each year has been steadily increasing. For the years 1970 through the projection of 2014, the number of men receiving degrees (in thousands) is given by the equation y = 3.6x + 441, and for women, the equation is y = 14.1x + 314, where x is the number of years after 1970.

a. Use the substitution method to solve this system of equations.

The solution of the system is (Type an ordered pair. Do not round until the final answer. Then round each coordinate to the nearest integer as needed.)

Solution

The problem involves solving a system of equations using substitution. The equations given are: 1. \( y = 3.6x + 441 \) 2. \( y = 14.7x + 314 \) We need to find the value of \( x \) and \( y \) where these two equations intersect. First, we can set the equations equal to each other because they both equal \( y \): \[ 3.6x + 441 = 14.7x + 314 \] Subtract \( 3.6x \) from both sides: \[ 441 = 11.1x + 314 \] Subtract 314 from both sides: \[ 127 = 11.1x \] Divide both sides by 11.1 to solve for \( x \): \[ x = \frac{127}{11.1} \approx 11.44 \] Since it asks for an integer, round \( x \) to 11. Now substitute \( x = 11 \) back into the first equation to find \( y \): \[ y = 3.6(11) + 441 \] \[ y = 39.6 + 441 \] \[ y = 480.6 \] Round to the nearest integer: \( y = 481 \). The solution to the system is approximately: \[ (x, y) = (11, 481) \]