Name: Linear Equations With One or More Variables
Uploaded: 2019-07-19
Duration: 11 min 20 s
Description: Let's learn the concept of linear equations, the introduction of linear algebra, the formation of linear equations in one, two and three variables, etc.

Question

Are the following pairs of linear equations consistent? Justify your answer.

$x + 2 y - 3 = 0$

$6 y + 3 x - 9 = 0$

Accepted Answer

A pair of linear equations will be consistent if they have at least one solution. This means that representing the linear equations will either be coincident lines or overlap each other or they will have unique solution between them. The condition for two lines to be consistent is $x + 2 y - 3 = 0$ (infinitely many solution) or $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$ (intersecting lines)

Given system of equations are:

$x + 2 y - 3 \Rightarrow x + 2 y = 3$ ----(i)

$6 y + 3 x - 9 = 0 \Rightarrow 3 x + 6 y = 9$ -----(ii)

We shall compare the coefficients of the pair of equations (i) and (ii) with the standard form:

$a_{1} x + b_{1} y = c_{1} a_{2} x + b_{2} y = c_{2}$

We get, $\frac{a_{1}}{a_{2}} = \frac{1}{3}, \frac{b_{1}}{b_{2}} = \frac{2}{6} = \frac{1}{3}$ and $\frac{c_{1}}{c_{2}} = \frac{3}{9} = \frac{1}{3}$ .

Here, we observe that, $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$ .

Hence, the lines represented by the given pair of linear equations are coincident lines having infinitely many solutions.

Therefore, the equations are consistent.

Are the following pairs of linear equations consistent? Justify your answer.

$x + 2 y - 3 = 0$

$6 y + 3 x - 9 = 0$

Important Questions on Pair of Linear Equations in Two Variables

Learn and Prepare for any exam you want !

Are the following pairs of linear equations consistent? Justify your answer. x+2y-3=0 6y+3x-9=0

Important Questions on Pair of Linear Equations in Two Variables

Learn and Prepare for any exam you want !

Are the following pairs of linear equations consistent? Justify your answer.

$x + 2 y - 3 = 0$

$6 y + 3 x - 9 = 0$