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Question

The pair of linear equations are
2x−3y=6
x2+y3=1

A
Parallel
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B
Coplanar
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C
Identical
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D
Perpendicular
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Solution

The correct options are
C Perpendicular
D Coplanar
To draw the graph for the given linear equation, we need to first plot the points which lie on it, join them to get a straight line.
First equation is 2x3y=6y=23x2
Substitute different values of x in the equation and calculate to get corresponding values of y.
x
y=23x2
Point (x,y)
0
2(0,2)
3 0(3,0)
6 2(6,2)
3 4(3,4)
6 6(6,6)
Second equation is x2+y3=1y=32x+3
Substitute different values of x in the equation and calculate to get corresponding values of y.
x
y=32x+3
Point (x,y)
0
3(0,3)
2 0(2,0)
4 3(4,3)
2 6(2,6)
4 9(4,9)
Plot these points on the graph paper and join them using a straight line.
On observing the graph, we find that the two lines intersect each other at right angle. Hence, they are perpendicular to each other.
204106_197920_ans.png

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