Question: ALGEBRA 1-B SEC25 PER03 4-2 Homework (LMS graded) Part 1 of 2 The number of men and women receiving…

ALGEBRA 1-B SEC25 PER03 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 the substitution method. The equations provided in the image are: For men: \( y = 3.6x + 441 \) For women: \( y = 4.1x + 314 \) Set the two equations equal to each other to find \( x \): \[ 3.6x + 441 = 4.1x + 314 \] Subtract \( 3.6x \) from both sides: \[ 441 = 0.5x + 314 \] Subtract 314 from both sides: \[ 127 = 0.5x \] Divide both sides by 0.5 to solve for \( x \): \[ x = 254 \] Substitute \( x = 254 \) back into the equation for men to solve for \( y \): \[ y = 3.6(254) + 441 \] Calculate: \[ y = 914.4 + 441 \] \[ y = 1355.4 \] Since we need to round each coordinate to the nearest integer: The solution is \( (254, 1355) \).