Question

Question 11 (ii)
By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve then.
X – 2y = 6, 3x – 6y = 0

Answer 1

given pair of equation is
x – 2y = 6
and 3x – 6y = 0
on comparing with ax +by + c = 0, we get
$a_1=1,b-1=-2and{c}_1=-6[fromEQ.(i\left)\right]a_2=3,b_2=-6and{c}_2=0[fromEq.(ii\left)\right]here,\frac{a_1}{a_2}=\frac{1}{3},\frac{b_1-2}{b_2-6}=\frac{1}{3}and\frac{c_1}{c_2}=\frac{-6}{0}\therefore \frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$
Hence, the lines represented by the given equations are parallel. Therefore, it has no solution. So, the given pair of lines is consistent.
Now, x + y = 3 $\Rightarrow$ y = 3 –x
If x = 0. Then y = 3, if x = 3, then y = 0
$\begin{array}{ccc}X& 0& 3\\ Y& 3& 0\\ Points& A& B\end{array}$
And 3x + 3y = 9 $\Rightarrow$ 3y = 9 – 3x
$\Rightarrow Y=\frac{9-3x}{3}$
If x = 0, then y = 3, if x = 1, then y = 2 and if x = 3, then y = 0
$\begin{array}{cccc}X& 0& 1& 3\\ Y& 3& 2& 0\\ Points& C& 3& E\end{array}$

Plotting the points A (0, 3) and B (3, 0), we get the line AB. Again, plotting the points (0, 3) D (1, 2) and E (3, 0), we get the line CDE
We observe that the lines represented by Eqs. (i) and (ii) are coincident