Solve the system:
y = 3x – 10
3x – y = -4

The correct answer is: No solution

Here we have solve the system of equation and find x and y.
Firstly , we are given, y = 3x – 10 and 3x – y = -4
So we can write,
y= 3x – 10
y – 3x = - 10
- 3x + y = - 10
3x – y = 10 -------( 1)
3x – y = -4 --------(2)
Now , we have a1/a2
a1/a2 = 3/3 =1
and b1/b2 ,
b1/b2 = -1/-1 = 1
and c1/c2
c1/c2 = 10/-4= -5/2
so here,
1 = 1 ≠ -5/2
a1/a2 = b1/b2 ≠ c1/c2
therefore the system of equation of no solution.
The correct answer is No solution.
Or,
y = 3x – 10 …(i)
3x – y = -4 …(ii)
Substituting y from (i) in (ii), we get
3x – (3x – 10) = -4
-10 = -4
The statement -10 = –4  is false, so the system of equations has no solution.

In this question, we have to find the system of equation. If (a1/a2) = (b1/b2) = (c1/c2) then it is infinitely many solutions, if (a1/a2) = (b1/b2) ≠ (c1/c2) and if (a1/a2) ≠(b1/b2) then it is unique solution.