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Q. 131

Expert-verifiedFound in: Page 44

Book edition
6th

Author(s)
Sullivan

Pages
1200 pages

ISBN
9780321795465

The figure shows the graph of two parallel lines. Which of the following pairs of equations might have such a graph?

$\left(a\right)x-2y=3\phantom{\rule{0ex}{0ex}}x+2y=7\phantom{\rule{0ex}{0ex}}\left(b\right)x+y=2\phantom{\rule{0ex}{0ex}}x+y=-1\phantom{\rule{0ex}{0ex}}\left(c\right)x-y=-2\phantom{\rule{0ex}{0ex}}x-y=1\phantom{\rule{0ex}{0ex}}\left(d\right)x-y=-2\phantom{\rule{0ex}{0ex}}2x-2y=-4\phantom{\rule{0ex}{0ex}}\left(e\right)x+2y=2\phantom{\rule{0ex}{0ex}}x+2y=-1$

Equation $\left(c\right)x-y=-2\phantom{\rule{0ex}{0ex}}x-y=1$might have such graph

We are given a graph and set of equations

In the graph both the lines are parallel and hence will have equal slopes

Consider the equations

$\left(c\right)x-y=-2\phantom{\rule{0ex}{0ex}}x-y=1$

On further simplifying the equation we get

$y=x+2\phantom{\rule{0ex}{0ex}}y=x-1$

Both the equation has same slope might have such graph

Consider the equations

$\left(a\right)x-2y=3\phantom{\rule{0ex}{0ex}}x+2y=7\phantom{\rule{0ex}{0ex}}\left(b\right)x+y=2\phantom{\rule{0ex}{0ex}}x+y=-1\phantom{\rule{0ex}{0ex}}\left(d\right)x-y=-2\phantom{\rule{0ex}{0ex}}2x-2y=-4\phantom{\rule{0ex}{0ex}}\left(e\right)x+2y=2\phantom{\rule{0ex}{0ex}}x+2y=-1$

On simplifying the equation we get

$\left(a\right)y=\frac{x}{2}-\frac{3}{2}\phantom{\rule{0ex}{0ex}}y=-\frac{1}{2}x+\frac{7}{2}\phantom{\rule{0ex}{0ex}}\left(b\right)y=-x+2\phantom{\rule{0ex}{0ex}}y=-x-1\phantom{\rule{0ex}{0ex}}\left(d\right)y=x+2\phantom{\rule{0ex}{0ex}}y=x+2\phantom{\rule{0ex}{0ex}}\left(e\right)y=-\frac{1}{2}x+1\phantom{\rule{0ex}{0ex}}y=-\frac{1}{2}x+1$

Option a) both the lines have different slopes hence the lines cannot be parallel

option d) both the lines are identical hence cannot describe the given figure

Option b) and option e) are not consistent with the given graph.

Equation $\left(c\right)x-y=-2\phantom{\rule{0ex}{0ex}}x-y=1$might have such graph.

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