By the graphical method,find whether the following pair of equations are consistent or not. If consistent,solve them.
$3x + y + 4 = 0$
$6x - 2y + 4 = 0$

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(A) The given pair of equations is:
$3x + y + 4 = 0 .....(i)$
$6x - 2y + 4 = 0 .....(ii)$
Comparing with $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$:
$a_1 = 3, b_1 = 1, c_1 = 4$
$a_2 = 6, b_2 = -2, c_2 = 4$
Calculating ratios:
$\frac{a_1}{a_2} = \frac{3}{6} = \frac{1}{2}$
$\frac{b_1}{b_2} = \frac{1}{-2} = -\frac{1}{2}$
Since $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$,the lines intersect at a unique point. Therefore,the system is consistent.
For equation $(i)$,$y = -3x - 4$:
$x$$0$$-1$$-2$
$y$$-4$$-1$$2$

For equation $(ii)$,$2y = 6x + 4 \Rightarrow y = 3x + 2$:
$x$$-1$$0$$1$
$y$$-1$$2$$5$

Plotting these lines on a graph,they intersect at the point $(-1, -1)$. Thus,the solution is $x = -1, y = -1$.

Explore More

Similar Questions

For a pair of equations $2x + 3y = 1$ and $3x - 2y = 8$,in usual notations $a_{1}b_{2} - a_{2}b_{1} = \dots$

If $2x + 3y = 7$ and $3x + 2y = 3$,then the value of $x + y$ is ..........

The sum of the digits of a two-digit number is $9$. If $27$ is added to it,the digits of the number get reversed. The number is

The solution set of $2x + 3y = 5$ and $4x + ky = 10$ is an infinite set. The value of $k$ is ...........

The pair of equations $2x + 6y = 10$ and $3x + 9y - 15 = 0$ has..........

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo