Question

The number of men and women receiving bachelors 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=3.7x+441, and for women, the equation is y=14.4x+314, where x is the number of years after 1970 A. Use the substitution method to solve the system of equationsB.C. Sketch a graph of the system of equations, write a sentence describing the trends for men and women receiving bachelor degrees

Answer 1

(a)(12, 485)

Step-by-step explanation:

Part A

The number of men and women receiving degrees ( in thousands ) is given by the equations:

`\begin{gathered} y=3.7x+441\cdots(1) \\ y=14.4x+314\cdots(2) \end{gathered}`

Substitute Equation(2) into Equation(1):

`14.4x+314=3.7x+441`

Next, solve for x:

`\begin{gathered} 14.4x-3.7x=441-314 \\ 10.7x=127 \\ x=(127)/(10.7) \\ x=11.9 \\ x\approx12 \end{gathered}`

Next, solve for y:

`\begin{gathered} y=3.7x+441=3.7(12)+441=485.4 \\ y\approx485 \end{gathered}`

The solution of the system is (12, 485).

Part B

12 years after 1970, i.e In 1982, the same number of men and women (485,000) received degrees.

Part C

The graph of the two equations is presented below:

The green line represents the number of men while the red line represents the number of women.

Between 1970 through 2014, initially, the number of men receiving degrees was higher in 1970 (at x=0), however, after 1982, the number of women receiving degrees was more than men.