Question

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 + 443, and for women, the equation is y = 14.3x + 317, where x is the number of years since 1970.

Use substitution to solve this system of equations.

Select one:
a. (42, 596)
b. (12, 485)
c. (71, 699)
d. (7, 468)

Answer 1

the actual answer is (13, 496)

Explanation:

Answer 2

b. (12, 485)

Explanation:

We have been given the number of men receiving degrees (in thousands) is given by the equation
`y=3.6x+443`, and for women, the equation is
`y=14.3x+317`, where x is the number of years since 1970.

Let us find the coordinates of the point of intersection of both lines by equating our both equations as:

`14.3x+317=3.6x+443`

`14.3x-3.6x+317=3.6x-3.6x+443`

`10.7x+317=443`

`10.7x+317-317=443-317`

`10.7x=126`

`(10.7x)/(10.7)=(126)/(10.7)`

`x=11.7757`

Upon substituting x=11.7757 in our equations we will get,

`y=3.6x+443`

`y=3.6*11.7757+443`

`y=42.39252+443`

`y=485.39252`

`y=14.3x+317`

`y=14.3*11.7757+317`

`y=168.3925+317`

`y=485.3925`

Upon rounding our answers to nearest whole number we will get,

`y=485.3925\approx 485`

`x=11.7757\approx 12`

Therefore, the point (12,485) will be the solution of our given equations and option b is the correct choice.