Question

Identify the system of equations: $4x+9y-11=0$ and $-2x-y-10=0$

• A. consistent
• B. inconsistent
• C. dependent
• D. no solution

Answer 1

The correct option is A consistent

The general form for a pair of linear equations in two variables $x$ and $y$ is
$a_{1}x+b_{1}y+c_1=0$ and
$a_{2}x+b_{2}y+c_2=0$
Let $4x+9y-11$....(1)
and $-2x-y-10$ ....(2)
Comparing equations (1) and (2) with the general form of equation to consider their co-efficient,
$a_1=4,a_2=-2,b_1=9,b_2=-1$
So, $\frac{4}{-2}\ne \frac{9}{-1}$
We know that $\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$ is said to be consistent.
Hence, the equations are consistent.