The solution set of a pair of equations x+y-1 | vedclass

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(D) Given equations are $x+y-1=0$ and $2x+2y-2=0$.Comparing with $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$,we have $a_1=1, b_1=1, c_1=-1$ and $a_2=2, b_

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infinite set

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(D) Given equations are $x+y-1=0$ and $2x+2y-2=0$.Comparing with $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$,we have $a_1=1, b_1=1, c_1=-1$ and $a_2=2, b_2=2, c_2=-2$.Calculating the ratios: $\frac{a_1}{a_2} = \frac{1}{2}$,$\frac{b_1}{b_2} = \frac{1}{2}$,and $\frac{c_1}{c_2} = \frac{-1}{-2} = \frac{1}{2}$.Since $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$,the lines are coincident.Coincident lines have infinitely many solutions,meaning the solution set is an infinite set.

The solution set of a pair of equations $x+y-1=0$ and $2x+2y-2=0$ is $\ldots \ldots \ldots \ldots$

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