Question

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

Answer 1

multiply second by 2
then add them
emit y
so you will find x
then put x into one of the equation
so you will have value of y

Answer 2

3x+2y=4
2x-y=5 ----> 4x-2y=10

adding
3x+2y+4x-2y=4+10
7x=14
x=2
now put x=2 in one of them
3x+2y=4
3(4)+2y=4
2y=4-12
2y=-8
y=-4

Answer 3

so it has one solution right?

Answer 4

you can also check it by just comparing coefficients
for eg...
ax+by+c=0 ......(1)
dx+ey+f=0....(2)
if a/d is not equal to b/e
then equations has only one solution
if a/d is equal to b/e which is not equal to c/f
the equations has no solutions
if all are equal in above case the it is coincident