Question

19. Does the following system have a unique solution? Why?4x-6y=-7-2x + 3y = 18

Answer 1

Given,

The equations are

$\begin{gathered} 4x-6y=-7..............(1) \\ -2x+3y=18............(2) \end{gathered}$

To find: Does the following system have a unique solution? Why?

Solution:

The determinant of the given equations are

$\begin{gathered} \begin{bmatrix}{4} & {-6} \\ {-2} & {3}\end{bmatrix}=\begin{bmatrix}{-7} & {} \\ {18} & {}\end{bmatrix} \\ 4\times3-(-6\times-2) \\ =12-12 \\ =0 \end{gathered}$

For unique solutions, the condition is

$\begin{gathered} \frac{a_1}{a_2}=\frac{b_1}{b_2} \\ \frac{4}{-2}=\frac{-6}{3} \\ -2=-2 \end{gathered}$

Condition satisfied.

Hence, the given equations have a unique solution.