By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve them.$x+y=3$$3 x+3 y=9$

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Given:

Pair of linear equations:

$x+y=3$

$3 x+3 y=9$

To do:

We have to find whether the given pair of linear equations is consistent /inconsistent. If consistent, then obtain the solution graphically.

Solution:

$x+y-3=0$.........(i)

$3x+3y-9=0$.........(ii)

Here,

$a_{1}=1, b_{1}=1, c_{1}=-3$

$a_{2}=3, b_{2}=3, c_{2}=-9$

$\frac{a_{1}}{a_{2}}=\frac{1}{3}$

$\frac{b_{1}}{b_{2}}=\frac{1}{3}$

$\frac{c_{1}}{c_{2}}=\frac{-3}{-9}$

$=\frac{1}{3}$

$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}}=\frac{c_1}{c_2}$

This implies,

The given pair of lines is coincident and therefore consistent.

For equation (i),

$y=3-x$

 $x$ 0 $3$ $y$ $3$ $0$

Plot point $( 0,\ 3)$ and $(3,\ 0)$ on a graph and join then to get equation $x+y=3$

For equation (ii),

$3y=9-3x$

$y=3-x$

 $x$ $0$ 3 $y$ $3$ 0

Plot points $(0,\ 3)$ and $(3,\ 0)$ on a graph and join them to get equation $3x+3y=9$

There are infinite solutions as the lines are coincident.

Updated on 10-Oct-2022 13:27:19