Question

Check whether the system of equation is inconsistent:

$4x+y=23$ and $8x+2y=10$

• A. inconsistent
• B. consistent
• C. dependent
• D. non-linear

Answer 1

The correct option is A inconsistent

Given, $4x+y=23$ and $8x+2y=10$
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
$4x+y=23$---(1)
$8x+2y=10$---(2)
Comparing equations (1) and (2) with the general form of equation to consider their co-efficient,
$a_1=4$ , $a_2=8$ , $b_1=1$ , $b_2=2$ , $c_1=23$ , $c_2=10$
Now, ratio of coefficient => $\frac{4}{8}=\frac{1}{2}\ne \frac{23}{10}$
We know that when $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$ then equations are said to be inconsistent.
Hence, the equations are inconsistent.