Mathematics with applications in the management, natural, and social sciences twelfth edition
chapter 6: systems of linear equations and matrices
6.1 exercises
19.) the number of baby boomers has been decreasing and the number of millennials has been increasing. now millenials have surpassed boomers in number. the following equations approximate the population y (in millions) of the given generation in year x, where x = 14 corresponds to the year 2014. (data from: pew research center.)
boomers: 10x+13y = 1125 millenials: -2x+7y = 495
solve this system of equations, and interpret your answer

answer: all the values are within because it has a pattern that repeats from -6 to 4.

good luck!

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

the answer would be 150 books

step-by-step explanation:

if you divide 300 by 2 you will get 150

answer: bea's uncle is 25 years old.

step-by-step explanation:

given the equation , we can say that the variable "x" represents the age of bea's uncle. then to find his age, we need to solve for "x":

we must add 15 to both sides of the equation:

now we need to divide both sides of the equation by 3:

therefore, we can conclude that bea's uncle is 25 years old.