Question

Solve the equation: $3x+y=6$ and $6x+2y=3$ and then identify the system of equation.

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

Answer 1

The correct option is B Inconsistent

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
$a_{2}x+b_{2}y+c_2=0$
$3x+y=6$ ----- (1)
$6x+2y=3$----- (2)
Comparing equations 1 and 2 with the general form of equation to write their co-efficient,
$a1=3;a2=6;b1=1;b2=2;c1=6;c2=3$
Compare the ratio, $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
$\frac{3}{6}=\frac{1}{2}=\frac{6}{3}$
If $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$, then the pair of linear equations has exactly one solution.
So, $\frac{1}{2}\ne \frac{6}{3}$ it said to be consistent.