Question

What are the classifications of each system? Drag the answer into the box to match each system. {4x−2y=102x−y=5 {y=2x−3−2x+y=−5 {2x−5y=143x+4y=10

Answer 1

The first one is. coincident 
second. inconsistent 
third. consistent independent 

I just did this quiz (: 

Answer 2

we know that

If a system has exactly one solution, it is a consistent independent system.

If a system has an infinite number of solutions, it is a consistent dependent system .

If a system has no solution, it is said to be inconsistent

We're going to solve each system to determine its classification

case A)

$4x-2y=10$ ------> equation A

$2x-y=5$ ------> equation B

Multiply equation B by $2$ both sides

$2*(2x-y)=2*5$ -----> $4x-2y=10$

Equation A and equation B are the same line

Therefore

The system has an infinite number of solutions

The answer case A) is

The system is a consistent dependent system (coincident)

case B)

$y=2x-3$ ------> equation A

$-2x+y=-5$ ------> equation B

Isolate the variable y in the equation B

$y=2x-5$

Both lines are parallel lines, because has the same slope

Therefore

The system has no solution

the answer case B) is

The system is inconsistent

case C)

$2x-5y=14$ ------> equation A

$3x+4y=10$ ------> equation B

Multiply equation A by $4$ and equation B by $5$ both sides

$4*(2x-5y)=4*14$ -----> $8x-20y=56$

$5*(3x+4y)=5*10$  -----> $15x+20y=50$

Adds the equations

$8x-20y=56 \\15x+20y=50\\-------\\8x+15x=56+50 \\23x=106 \\x=4.61$

Find the value of y

$2*4.6-5y=14$

$y=-0.96$

therefore

The system has one solution

The answer case C) is

The system is a consistent independent system