Consistent and independent system of two linear equations is a system such that there is only one solution for the system, that is, the two straight lines cross at a point. So we can analyze each case and I have attached some graphs to provided you with examples. Those graphs aren't about the equations but it's about general cases:

A) Consistent and dependent. If we divide this given equation by 2 we get the same line. (See Figure 1)

B) Inconsistent. No solutions. (See Figure 2)

C) Consistent and Independent. (See Figure 3)

D) Consistent and dependent.

7 0

2 years ago

Read 2 more answers

At the football game, 4 hamburgers and 6 soft drinks cost $34, and 4 hamburgers and 3 soft drinks cost $25. Which two equations

olga_2 [115]

Answer:

$4x+6y=34\\\\4x+3y=25$

Step-by-step explanation:

Let be "x" the cost in dollars of a hamburger and "y" the cost in dollars of a soft drink.

The cost of 4 hamburguers can be represented with this expression:

$4x$

And the cost of 6 soft drinks can be represented with this expression:

$6y$

Since the total cost for 4 hamburgers and 6 soft drinks is $34, you can write the following equation:

$4x+6y=34$ [Equation 1]

The following expression represents the the cost of 3 soft drinks:

$3y$

According to the information given in the exercise, the total cost for 4 hamburgers and 3 soft drinks is $25. Then, the equation that represents this is:

$4x+3y=25$ [Equation 2]