Which of the following pairs of linear equati | vedclass

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(A) Given equations are $2x + y - 6 = 0$ and $4x - 2y - 4 = 0$.Comparing with $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$:$a_1 = 2, b_1 = 1, c

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Consistent

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(A) Given equations are $2x + y - 6 = 0$ and $4x - 2y - 4 = 0$.Comparing with $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$:$a_1 = 2, b_1 = 1, c_1 = -6$$a_2 = 4, b_2 = -2, c_2 = -4$Calculating ratios:$\frac{a_1}{a_2} = \frac{2}{4} = \frac{1}{2}$$\frac{b_1}{b_2} = \frac{1}{-2} = -\frac{1}{2}$Since $\frac{a_1}{a_2} 
eq \frac{b_1}{b_2}$,the lines intersect at a unique point,meaning the system is consistent.For $2x + y - 6 = 0 \implies y = 6 - 2x$:If $x=0, y=6$; if $x=1, y=4$; if $x=2, y=2$.For $4x - 2y - 4 = 0 \implies y = 2x - 2$:If $x=0, y=-2$; if $x=1, y=0$; if $x=2, y=2$.The lines intersect at $(2, 2)$.

Which of the following pairs of linear equations are consistent/inconsistent? If consistent,obtain the solution graphically: $2x + y - 6 = 0, 4x - 2y - 4 = 0$.

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