Classify each system. the system shown below is . x + 3y = 4 3x + 9y = 12 the system shown below is . 3x – 4y = 12 6x – 8y = 21 the system shown below is . 2x – 3y = 8 –3x + 2y = 8

The first one is consitent and dependent

The second one is inconsistent

The third one is consistent and independent

The first system is consistent & dependent; the second system is inconsistent; and the third system is consistent & independent.

Step-by-step explanation:

A consistent system is a system that has at least one solution.  A dependent system is a system that has infinite solutions, because the equations describe the same line.  An independent system is a system that has one solution.  

An inconsistent system is a system that has no solution because the lines are parallel.

The first system is

To solve this, we would make the coefficients of y the same.  We would do this by multiplying the top equation by 3:

We have the same equation; thus this system is consistent and dependent.

The second system is

To solve this, we will make the coefficients of x the same; we will do this by multiplying the top equation by 2:

We have two equations that have the same slope but different y-intercepts; these lines are parallel and thus are inconsistent.

The third system is

To solve this, we will make the coefficients of x the same; we will do this by multiplying the top equation by 3 and the bottom equation by 2:

Now we will add the two equations:

Divide both sides by -5:

-5y/-5 = 40/-5

y = -8

Now substitute this into the first equation:

2x-3(-8) = 8

2x+24 = 8

Subtract 24 from each side:

2x+24 - 24 = 8-24

2x = -16

Divide both sides by 2:

2x/2 = -16/2

x = -8

The solution is (-8, -8); thus the system is consistent and independent.

the ratio of grapes to blueberries she should use is 12: 3

step-by-step explanation:

if mandie is making 15 cups of fruit salad, the ratio of grapes to blueberries she should use is 12: 3.

the answer is d on edge

step-by-step explanation: