Question

Solve the equation: $4x-16y=7$ and $x-4y=2$8 and then identify the system of equation.

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

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
$a_{2}x+b_{2}y+c_2=0$

$4x-16y=7$ ----- (1)
$x-4y=28$----- (2)

Comparing equations (1) and (2) with the general form of equation to write their co-efficient,

$a_1=4;a_2=1;b_1=-16;b_2=-4;c_1=7;c_2=28$

Compare the ratio, $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
$\frac{4}{1}=\frac{-16}{-4}=\frac{7}{28}$
If $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$, then the pair of linear equations has exactly one solution.
So, $4=4=4$ it said to be consistent.