Consider the system of equations. 5x + 2y = 6, 10x + 4y = 12 which equation is equivalent to the first equation of the system and can be used to solve the system using the linear combination method? which answer describes the number of solutions to the system of equations?

You have infinite solutions to the system, and those can be obtained by the relation y = 3 - (5/2)*x where you can give any value for x.

Step-by-step explanation:

The equations that we have are:

5x + 2y = 6 and 10x + 4y = 12

First, you can see that the second equation is equal to the first equation multiplied by a factor of 2:

2*(5x + 2y) = 2*6

10x + 4y = 12

this means that the equations are not linear independent, so in this case, we have only one equation that has information and two variables, because we have fewer equations than variables, we have infinite possible solutions of our system.

for solving this we can do:

5x + 2y = 6

2y = 6 - 5x

y = 3 - (5/2)*x

now, you an give value to x, and from this, you get the value of y.

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.