Gizmo Warm-up The equations x + y = 8 and x – y = 2 form a system of
linear equations in standard form. In the Solving Linear
Systems (Matrices and Special Solutions) Gizmo, you can
use graphing or algebra to solve such systems.
On the CONTROLS tab, select the top equation. Set A to
1, B to 1, and C to 8 to graph x + y = 8. Select the bottom
equation. Set A to 1, B to –1, and C to 2 to graph x – y = 2.
(To quickly set the value of a slider, type the number into
the text box to the right of the slider and press Enter.)
1. Look at the graph. How many points of intersection do the lines have?
2. Mouseover the purple intersection point. What are the coordinates? ( , )
3. How do these values relate to Max and Mary’s ages?

When booking personal travel by air, one is always interested in actually arriving at one’s final destination even if that arrival is a bit late. the key variables we can typically try to control are the number of flight connections we have to make in route, and the amount of layover time we allow in those airports whenever we must make a connection. the key variables we have less control over are whether any particular flight will arrive at its destination late and, if late, how many minutes late it will be. for this assignment, the following necessarily-simplified assumptions describe our system of interest: the number of connections in route is a random variable with a poisson distribution, with an expected value of 1. the number of minutes of layover time allowed for each connection is based on a random variable with a poisson distribution (expected value 2) such that the allowed layover time is 15*(x+1). the probability that any particular flight segment will arrive late is a binomial distribution, with the probability of being late of 50%. if a flight arrives late, the number of minutes it is late is based on a random variable with an exponential distribution (lamda = .45) such that the minutes late (always rounded up to 10-minute values) is 10*(x+1). what is the probability of arriving at one’s final destination without having missed a connection? use excel.