Solve the following pair of linear equations | vedclass

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(B) Given the equations: $1) \ 2x + 3y = 12$ $2) \ 2x + 3y = 6$ Comparing these equations with the standard form $a_1x + b_1y + c_1 = 0$ and $a_2x + b

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$\varnothing$ (No solution)

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(B) Given the equations: $1) \ 2x + 3y = 12$ $2) \ 2x + 3y = 6$ Comparing these equations with the standard form $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$,we have: $a_1 = 2, b_1 = 3, c_1 = -12$ $a_2 = 2, b_2 = 3, c_2 = -6$ Calculating the ratios: $\frac{a_1}{a_2} = \frac{2}{2} = 1$ $\frac{b_1}{b_2} = \frac{3}{3} = 1$ $\frac{c_1}{c_2} = \frac{-12}{-6} = 2$ Since $\frac{a_1}{a_2} = \frac{b_1}{b_2} 
eq \frac{c_1}{c_2}$,the lines are parallel to each other. Parallel lines do not intersect at any point,which means the system of equations has no solution. Therefore,the solution set is $\varnothing$.

Part $I$	Part $II$
$1. x+2y=3, 2x+4y=5$	$a. \text{Solution set is a singleton set.}$
$2. 2x+3y=6, x+\frac{3}{2}y=3$	$b. \text{Solution set is an empty set.}$
$3. 3x-y=0, x-y+6=0$	$c. \text{Solution set is an infinite set.}$
	$d. \text{Solution set contains two members.}$

Solve the following pair of linear equations in two variables graphically: $2x + 3y = 12$ and $2x + 3y = 6$.

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