Question

Which equations have one solution

Answer 1

Answer:   C and  F

Step-by-step explanation:

Remember that for two equations to have the same solutions they need to have the different slopes and different y intercepts or they could have the same y-intercepts but different slopes.

First we will simply each of the equations  

A.  $\frac{1}{3} x + 3 = 26 + \frac{6}{18}x - 23$   reduces to .$\frac{1}{3}x + 3 = \frac{1}{3} x + 3$   Since this have the same slopes and same y-intercept they have infinitely many solutions

B. x +3 + 3x = -3 +4x +6  reduces to 4x + 3 = 4x +3  This also have the same slopes and same y-intercepts which means it also have infinitely many solutions.

C. 2(1/5 + 1/4x) -2x = x -1  reduces to  -3/2x +2/5 = x -1   This have different slopes and different y intercepts so they have One solution.

D . 4.3x + 2.5 -2.2x + 2.2 -2.1x = 0   reduces to  4.7 = 0  which means that this equation have no solution because 4.7 does not equal 0.  

E. 2(4x +3) + 2x= 5(2x + 3)    reduces to  10x + 6 = 10x + 15   which means this also have No solution because they have the same slopes but different  y-intercepts.

F.  2/5x + 10 + 3/5x = 2x + 5 reduces to 1x + 10 = 2x + 5   This also have 1 solution because they have different slopes and different y intercepts.