Question

3x + 2y = 4
2x - y = 5
This system of equations
A)has no solution.
B)has one solution.
C)is coincident.

Answer 1

3x + 2y = 4
2x - y = 5 times second equation by 2
4x-2y=10
adding equation 1 and new equation
7x=14
x=2
put in eq 1
3(2)+2y=4

6+2y=4
2y=-2
y=-1
option b is right 

Answer 2

we have

$3x+2y=4$ ----> equation A

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

Multiply the equation B by $2$

$2(2x-y)=2*5$

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

Adds equation A and equation C

$3x+2y=4 \\4x-2y=10\\---------- \\4x+3x=4+10 \\7x=14 \\x=2$

find the value of y

$2*2-y=5$

$y=4-5=-1$

the solution is the point $(2,-1)$

therefore

the answer is the option B

has one solution