Question

Q.4 For each of the following system of equations find whether it has unique solution, infinite number of solutions or no solutions.

$2x-3y=6,x+y=1$

Answer 1

Step 1: Given Equations

Understanding and Applying

The given system of equations may be written as

$2x-3y-6=0,x+y-1=0$

The given system of equations is of the form

$$\begin{gathered} a_{1}x+b_{1}y+c_1=0 \\ {a}_{2}x+b_{2}y+c_2=0 \end{gathered}$$

Step 2:Given values

$$\begin{gathered} a_1=2,b_1=-3,c_1=-6 \\ {a}_2=1,b_2=1,c_2=-1 \end{gathered}$$

Step 3: Equating the coefficients of the given equation

We have

$\frac{a_1}{a_2}=\frac{2}{1},\frac{b_1}{b_2}=\frac{-3}{1}\frac{c_1}{c_2}=\frac{-6}{-1}=\frac{6}{1}$

Step 4: Result

Clearly,

The given system of equations has a unique solution.