Question

Question 11 (i)
By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve then.
3x+y+4 = 0, 6x – 2y + 4 = 0

Answer 1

3x + y 4 = 0
and 6x – 2y+ 4 =0
on comparing with ax + by + c = 0, we get
$a_1=3,b_1=1and{c}_1=4a_2=6,b_2=-2and{a}_2=6,b_2=-2c_2=4here\frac{a_1}{a_2}=\frac{3}{6}=\frac{1}{2}\frac{b_1}{b_2}=and\frac{c_1}{c_2}=\frac{4}{4}=\frac{1}{1}\therefore \frac{a_1}{a_2}\ne \frac{b_1}{b_2}$
So, the given pair of linear equations are intersecting at one point, therefore these lines have unique solution.
Hence, given pair of linear equations is consistent
We have, 3x + y + 4 = 0
$\Rightarrow$ y =-4 - 3x
When x = 0, then y = - 4
When x = - 1, then y = - 1
When x = - 2, then y = 2
$\begin{array}{cccc}X& 0& -1& -2\\ Y& -4& -1& 2\\ Points& B& C& A\end{array}$
and 6x – 2y + 4 = 0
$\Rightarrow$ 2y = 6x + 4
$\Rightarrow$ y = 3x + 2
When x = 0, then y = 2
When x = - 1, then y = - 1
When x = 1, then y = 5
$\begin{array}{cccc}X& -1& -1& -2\\ Y& -1& -1& 2\\ Points& C& Q& P\end{array}$
Plotting the points B (0, - 4) A (-2, 2) we get the straight tine AB. Plotting the points Q (Q, 2) and P (1, 5), we get the straight line PQ. The lines AB and PQ PQ intersect at C (-1, -1)