Question

Solve the equation: $2x-y=1$ and $2x+3y=3$ and then identify the system of equation.

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

Answer 1

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