Question

Solve the equation: $\frac{1}{4}x+11y=9$ and $x+44y=36$ and then identify the system of equation.

• A. Consistent
• B. Inconsistent
• C. Dependent
• D. All the above

Answer 1

The correct option is C Dependent

By using conditions for consistency of linear equation:

Let us consider 2 linear equations $ax+by+c=0$ and $mx+ny+p=0$

if $\frac{a}{m}=\frac{b}{n}=\frac{c}{p}$ then system of equation is dependent

So comparing it with given equations we get,

$\frac{\frac{1}{4}}{1}=\frac{11}{44}=\frac{9}{36}$

$⟹\frac{1}{4}=\frac{1}{4}=\frac{1}{4}$

Hence system of equation is dependent.

mx+ny+Then above equation are dependent if