Chapter 1: Q. 131 (page 44)

The figure shows the graph of two parallel lines. Which of the following pairs of equations might have such a graph?
$(a) x - 2 y = 3 x + 2 y = 7 (b) x + y = 2 x + y = - 1 (c) x - y = - 2 x - y = 1 (d) x - y = - 2 2 x - 2 y = - 4 (e) x + 2 y = 2 x + 2 y = - 1$

Short Answer

Expert verified

Equation $(c) x - y = - 2 x - y = 1$ might have such graph

Step by step solution

Given information

We are given a graph and set of equations

Explanation for correct options

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

Consider the equations

$(c) x - y = - 2 x - y = 1$

On further simplifying the equation we get

$y = x + 2 y = x - 1$

Both the equation has same slope might have such graph

Explanation for other explanations

Consider the equations

$(a) x - 2 y = 3 x + 2 y = 7 (b) x + y = 2 x + y = - 1 (d) x - y = - 2 2 x - 2 y = - 4 (e) x + 2 y = 2 x + 2 y = - 1$

On simplifying the equation we get

$(a) y = \frac{x}{2} - \frac{3}{2} y = - \frac{1}{2} x + \frac{7}{2} (b) y = - x + 2 y = - x - 1 (d) y = x + 2 y = x + 2 (e) y = - \frac{1}{2} x + 1 y = - \frac{1}{2} x + 1$

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.

Conclusion

Equation $(c) x - y = - 2 x - y = 1$ might have such graph.

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The figure shows the graph of two parallel lines. Which of the following pairs of equations might have such a graph?
$(a) x - 2 y = 3 x + 2 y = 7 (b) x + y = 2 x + y = - 1 (c) x - y = - 2 x - y = 1 (d) x - y = - 2 2 x - 2 y = - 4 (e) x + 2 y = 2 x + 2 y = - 1$

Short Answer

Step by step solution

Given information

Explanation for correct options

Explanation for other explanations

Conclusion

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The figure shows the graph of two parallel lines. Which of the following pairs of equations might have such a graph?(a)x-2y=3x+2y=7(b)x+y=2x+y=-1(c)x-y=-2x-y=1(d)x-y=-22x-2y=-4(e)x+2y=2x+2y=-1

Short Answer

Step by step solution

Given information

Explanation for correct options

Explanation for other explanations

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Discrete Mathematics

Pure Maths

Logic and Functions

Decision Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

The figure shows the graph of two parallel lines. Which of the following pairs of equations might have such a graph?
$(a) x - 2 y = 3 x + 2 y = 7 (b) x + y = 2 x + y = - 1 (c) x - y = - 2 x - y = 1 (d) x - y = - 2 2 x - 2 y = - 4 (e) x + 2 y = 2 x + 2 y = - 1$