Write an equation of a line passing through the point representing the solution of the pair of linear equations $x+y=2$ and $2x-y=1$. How many such lines can we find?

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(D) First,we solve the pair of linear equations:
$x + y = 2$ --- $(i)$
$2x - y = 1$ --- $(ii)$
Adding equations $(i)$ and $(ii)$,we get:
$(x + y) + (2x - y) = 2 + 1$
$3x = 3$
$x = 1$
Substituting $x = 1$ in equation $(i)$:
$1 + y = 2$
$y = 1$
The solution point is $(1, 1)$.
Any line passing through $(1, 1)$ can be written in the form $y - 1 = m(x - 1)$,where $m$ is the slope. For example,if $m = 1$,the equation is $y - 1 = x - 1$,which simplifies to $y = x$.
Since there are infinitely many possible values for the slope $m$,there are infinitely many such lines that can pass through the point $(1, 1)$.

Explore More

Similar Questions

Solve the following pairs of equations by the cross-multiplication method:
$0.5x + 0.3y = 0.1$
$0.6x + 0.3y = 0.3$

The angles of a cyclic quadrilateral $ABCD$ are $\angle A = (6x + 10)^{\circ}$,$\angle B = (5x)^{\circ}$,$\angle C = (x + y)^{\circ}$,and $\angle D = (3y - 10)^{\circ}$. Find $x$ and $y$,and hence the values of the four angles.

Difficult
View Solution

The solution of a pair of equations $y+x=2$ and $y-x=4$ is $(x, y)=\ldots \ldots \ldots . . .$

If a pair of linear equations is consistent,then the lines will be

The ratio of the present ages of Rajan and Jay is $3:2$. After five years,the ratio of their ages will be $4:3$. Find the present ages of both.

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