3x + 2y = 4
2x - y = 5
(a) this system of equations has no solution.
(b) has one solution.
(c) is coincident.

3x + 2y = 4
2x - y = 5(2)

3x + 2y = 4
4x - 2y = 10 (result of multiplying by 2)
add
7x = 14
x = 2

2x - y = 5
2(2) - y = 5
4 - y = 5
-y = 5 - 4
-y = 1
y= 1

solution is : (2,1)one solution

3x + 2y = 4

2x -   y =     5      

From the second equation:

-y = 5 - 2x

y = 2x - 5

Substitute y = 2x - 5 into the first equation

3x + 2y = 4

3x + 2*(2x - 5) = 4

3x + 4x - 10 = 4

7x = 4 + 10

7x = 14           x = 14/7         x = 2.

Recall y = 2x - 5 = 2*2 - 5 = 4 - 5 = -1.

x = 2,  y = -1

B has one solution. 

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