Question

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

$x+2y=1,2x-3y=12$

Answer 1

Step 1:Given equations

Understanding & Applying

The given system of equations may be written as

$x+2y=1,2x-3y-12=0$

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

$$\begin{gathered} a_1=1,b_1=2,c_1=-1 \\ {a}_2=2,b_2=-3,c_2=-12 \end{gathered}$$

Step 3:Equating the Coefficients of the given equation

We have $\frac{a_1}{a_2}=\frac{1}{2},\frac{b_1}{b_2}=\frac{2}{-3},\frac{c_1}{c_2}=\frac{-1}{-12}=\frac{1}{12}$

Step 4: Result

Clearly,

a1 is not equal tp b1

b1 is not equal to b2

i.e,

$\frac{1}{2}isnotequalto\frac{2}{-3}$

Therefore ,the given system of equations has a unique solution