Question

For what value of a, the system of equations is inconsistent
ax + 3y = a - 3
12x + ay = a

Answer 1

The given system of equations is inconsistent for a=-6

Step-by-step explanation:

Given equations are $ax+3y=a-3\hfill (1)$

and $12x+ay=a\hfill (2)$

To find the value of a in which the given equations is inconsistent :

• That is show that the given equations has no solutions.
• Given line equations are parallel they have not any solutions .
• Then their  slopes are equal and intercepts are not equal

• The slope intercept form is y=mx+c
• Then we can write the given equations in the form
• so from equation (1) we have $y=\frac{-a}{3}x+\frac{a-3}{3}$  
• From equation (2) we have  $y=\frac{-12}{a}x+1$   

Equating the slopes m from equations (1) and (2) we get

• $\frac{-a}{3}=\frac{-12}{a}$
• $a(a)=12(3)$
• $a^2=36$
• $a=\pm 6$

Equating c from equations (1) and (2)

• $\frac{(a-3)}{3}\neq 1$ (since intercepts are not equal)
• $a-3\neq 3$
• $a\neq 6$

Therefore a = 6 is eliminated ( if a = 6 there will be infinite solutions for both equations they lie in the same line)

Therefore we take the value of a= -6 for which has no solutions

Hence the given system of equations is inconsistent for a=-6