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# identify the system of equality which has no solution

1. x-2y=-6

2x=4y-12

2. x+2y-1

2x+4y

3. 5x+2y=4

2x-2y+10

4. -x+3y+1

x+3y-1

### 2 Answers by Expert Tutors

Nataliya D. | Patient and effective tutor for your most difficult subject.Patient and effective tutor for your mos...
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I.  x - 2y = -6   .....(1)
2x = 4y - 12 ....(2)
Let's (2) by "2" and move "y" to the right side of an equation
x - 2y = -6 , so you can see, that (1) and (2) are identical.
The system has an infinite number of solutions.

II.
x = 2y - 1  ......(1)
2x =  4y    ......(2)
Let's divide (2) by "2" we will get
x = 2y      ......(2)
This system has no solutions. There is contradiction, from one side x = 2y - 1 and  from another side x = 2y

III. For this system let's use method of illumination:
5x + 2y = 4
+
2x - 2y = 10
‾‾‾‾‾‾‾‾‾‾‾‾‾‾
7x        = 14
x = 2
Let's plug in value of "x" into first equation
5 • (2) + 2y = 4
10 + 2y = 4
2y = - 6
y = - 3
The solution of the given system is pair of numbers (2, - 3)

IV.  - x = 3y + 1  .....(1)
x = 3y - 1   ....(2)
Let's live "3y" by itself for both equations
- x - 1 = 3y
—
x + 1 = 3y
‾‾‾‾‾‾‾‾‾‾‾‾‾
- 2x - 2 = 0

- 2x = 2
x = - 1
Let's plug in value of "x" into second equation
- 1 = 3y - 1
3y = 0
y = 0

The solution of the given system is pair of numbers (- 1, 0)

Michael S. | Math &amp; Science made FriendlierMath &amp; Science made Friendlier
4.8 4.8 (13 lesson ratings) (13)
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(2)

This system will not have a unique solution.  The slopes of the two lines are identical - so either they are parallel (and never intersect) or are identical lines (and an infinite number of identical points).

Its not quite possible to tell - as the second equation in the (2), (3) and (4) answers are all missing the equal sign.  But in the (3) and (4) case - one can see that the slopes are different - so they must intersect somewhere.

i wrote it wrong its

1. x-2y=-6

2x=4y-12

2. x=2y-1

2x=4y

3. 5x+2y=4

2x-2y=10

4. -x=3y+1

x=3y-1