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

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(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_

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empty set

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(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:

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