Graphically, the pair of equations $6 x − 3 y + 10 = 0 and 2 x − y + 9 = 0$ represents

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parallel lines

intersecting lines

perpendicular lines

None

answer is A.

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Detailed Solution

Given equations are

6 x − 3 y + 10 = 0 and 2 x − y + 9 = 0

.
We know that a straight line can be used to illustrate the graph of a linear equation by finding values of y for specified values of x.
Write the given two equations in the form of

y = a x + b

− 3 y = − 6 x − 10 y = − 6 x − 3 − 10 − 3 y = 2 x + 103 … … (1) − y = − 2 x − 9 y = − 2 x − 1 − 9 − 1 y = 2 x + 9 … … (2)

Find the x and y values for the equation (1).

x	-1	0	1	2
$y = 2 x + 103$	$2 (− 1) + 103 = 1.33$		$2 (0) + 103 = 3.33$		$2 (1) + 103 = 5.33$		$2 (2) + 103 = 7.33$

Find the x and y values for the equation (2).

x	-1	0	1	2
y = 2x + 9	2(-1) + 9 = 7	2(0) + 9 = 9	2(1) + 9 = 11	2(2) + 9 =13

Form the graphs of given two equations with obtained values of x and y.
Plot the obtained (x, y) values and join them to get the graphs of the respective equations.
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