Question

Solve the equation: $5x+y=-1$ and $-5x-y=0$ and then identify the system of equation

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

Answer 1

The correct option is C Dependent

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