Question

Solve the equation: $5x+6y=-1$ and $10x+12y=\frac{1}{2}$ 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
$a_{2}x+b_{2}y+c_2=0$
$5x+6y=-1$ ----- (1)
$10x+12y=\frac{1}{2}$----- (2)
Comparing equations 1 and 2 with the general form of equation to write their co-efficient,
$a1=5;a2=10;b1=6;b2=12;c1=-1;c2=\frac{1}{2}$
Compare the ratio, $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
$\frac{5}{10}=\frac{6}{12}=\frac{-1}{\frac{1}{2}}$
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, $\frac{6}{12}\ne \frac{-1}{\frac{1}{2}}$ it said to be consistent.