The solution of the pair of equations x+y-1=0 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given equations are:$1) x + y - 1 = 0 \implies x + y = 1$$2) 2x + 2y - 3 = 0 \implies 2x + 2y = 3$Comparing these with the general form $a_1x + b_

Vedclass · Accepted Answer

empty set

Vedclass · Answer

(C) Given equations are:$1) x + y - 1 = 0 \implies x + y = 1$$2) 2x + 2y - 3 = 0 \implies 2x + 2y = 3$Comparing these with the general form $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$:$a_1 = 1, b_1 = 1, c_1 = -1$$a_2 = 2, b_2 = 2, c_2 = -3$Now,calculate the ratios:$\frac{a_1}{a_2} = \frac{1}{2}$$\frac{b_1}{b_2} = \frac{1}{2}$$\frac{c_1}{c_2} = \frac{-1}{-3} = \frac{1}{3}$Since $\frac{a_1}{a_2} = \frac{b_1}{b_2} 
eq \frac{c_1}{c_2}$,the lines are parallel to each other.Therefore,the system of equations has no solution,which corresponds to an empty set.

The solution of the pair of equations $x+y-1=0$ and $2x+2y-3=0$ is:

Similar Questions

If the following pair of equations is consistent (unique solution),then find the value of $k$:
$x - ky = 2$
$3x + 2y = -5$

Find the value of $k$ under the given condition for the following pair of linear equations: $2x - 3y = 1$ and $kx + 5y = 7$,such that the system has a unique solution.

Solve the following pair of linear equations in two variables using a graph: $x + y = 5$ and $5x - 2y = 4$.

Solve the following pairs of equations by the cross-multiplication method:
$4x + 6y = 11$
$5x - 8y = 6$

Solve the following pair of linear equations by the cross-multiplication method:
$\frac{x}{a} + \frac{y}{b} = 0$
$(a+b)x + (a-b)y = a^2 + b^2$

Vedclass Test Series

Exam Paper Generator

Online Exam Module