Question

Q.1 For each of the following system of equations find whether it has unique solution, infinite number of solutions or no solutions.

x-2y=2, 4x-2y=5

Answer 1

Step 1:Given Equations

The given system of equations may be written as

$$\begin{gathered} x-2y-2=0\Rightarrow 1 \\ 4x-2y-5=0\Rightarrow 2 \end{gathered}$$

The given system of equations is if 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

$$\begin{gathered} valuesof{a}_1,b_1,c_1\&a_2,b_2,c_{2}are \\ where{a}_1=1,b_1=-2,c_1=-2 \\ {a}_2=4,b_2=-2,c_2=-5 \end{gathered}$$

Step 3:Equating the coefficients

We have

$\frac{a_1}{a_2}=\frac{1}{4},\frac{b_1}{b_2}=\frac{-2}{-2},\frac{c_1}{c_2}=\frac{-2}{-5}$

Step 4: Result

$$\begin{gathered} Clearly,\frac{a_1}{a_2}isnotequalto\frac{b_1}{b_2} \\ \frac{1}{4}isnotequalto\frac{-2}{-2} \end{gathered}$$

Conclusion: Therefore The given system of equation is consistent with unique solution.