Question

I have to use the substitution method to solve the system of equations.

4x-y=9 and 2x+3y=12

I worked this problem myself and could not find a possible solution. So I put that it is inconsistent. Is that correct? If not could you please help me?
from the 1st ---> 4x-9 = y
sub that into the 2nd

2x + 3(4x-9) = 12
2x + 12x - 27 = 12
14x = 39
x = 39/14
y = 4(39/14) - 9 = 15/7

check:
1st:
LS = 4(39/14) - 15/7
= 156/14 - 30/14
= 126/14 = 9 = RS
2nd:
LS = 2(39/14) + 3(15/7)
= 39/7+ 45/7
= 84/7 = 12 = RS

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