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37 votes
37 votes
The following system has no solution.

x+y +2 = 15
2x+2=1
2y -2=7

True or False

User Shatisha
by
2.9k points

2 Answers

21 votes
21 votes

Answer:

True

No solution

Explanation:

The system of equations is

x + y +2 = 15 (1)
2x + 2 = 1 (2)
2y - 2 = 7 (3)

Subtract 2 from both sides of Eq (2)

==> 2x + 2 - 2 = 1 - 2

==> 2x = -1

==> x = - 1/2 = - 0.5

Add 2 to both sides of Eq (3)

2y - 2 + 2 = 7 + 2

2y = 9

y = 9/2 = 4.5

Plug in values for x and y in Eq (1)

x + y + 2 = 15 becomes

- 0.5 + 4.5 + 2 = 15

==> 6 = 15 which is false

This is an inconsistent system of equations. and therefore has no solution

User NiMeDia
by
3.0k points
23 votes
23 votes
This is false because 2x+2=1 is a higher number
User Oleksandr Firsov
by
3.3k points