Which system of linear equations has NO solution?

Question

A)a-b=2

   b=-a-3

B) a-b=3

    a+b=-2

C)-a+b=-2

   b=a+3

D)a+b=3

   -a+b=2

Answer 1

Hi Valesia, if the system consists of parallel lines, there will be no solution. Put the lines in slope-intercept form, this is the easiest form to use. If the slope of the lines when in slope-intercept form are the same, the lines are parallel.

 

Solve for a:

 

A) 

 

a = b + 2

 

a = -b - 3

 

Slopes are 1 and -1, lines are not parallel

 

B)

 

a = b + 3

 

a = -b - 2

 

Slopes are 1 and -1, lines are not parallel

 

C)

 

a = b + 2

 

a = b + 3

 

Slopes are 1 and 1, the lines are parallel.

 

D)

 

a = -b + 3

 

a = b - 2

 

Slopes are -1 and 1, lines are not parallel.

 

Answer: C

 

Questions?

 

 

Answer 2

Hi Valesia,

 

Choice C. When you add them, you get 0 = -5.

Also, if you use substitution, it doesn't make sense. 

b = a+3

plug in -a+b=-2

-a+a+3 = -2

3 ≠ -2