Question

Solve the equation: $9x+3y=-4$ and $x+\frac{1}{3}y=3$ and then identify the system of equation.

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

Answer 1

Answer: (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
$a_{2}x+b_{2}y+c_2=0$
$9x+3y=-4$ ----- (1)
$6x+\frac{1}{3}y=3$----- (2)
Comparing equations 1 and 2 with the general form of equation to write their co-efficient,
$a1=9;a2=1;b1=3;b2=\frac{1}{3};c1=-4;c2=3$
Compare the ratio, $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
$\frac{9}{1}=\frac{3}{\frac{1}{3}}=\frac{-4}{3}$
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, $\frac{3}{\frac{1}{3}}\ne \frac{-4}{3}$ it said to be consistent.