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Sketch these three lines and decide if the equations are solvable: 3 by 2 system x + 2y

Chapter 1, Problem 1.2.4

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QUESTION:

Sketch these three lines and decide if the equations are solvable: 3 by 2 system x + 2y = 2 x y = 2 y = 1. What happens if all right-hand sides are zero? Is there any nonzero choice of righthand sides that allows the three lines to intersect at the same point?

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QUESTION:

Sketch these three lines and decide if the equations are solvable: 3 by 2 system x + 2y = 2 x y = 2 y = 1. What happens if all right-hand sides are zero? Is there any nonzero choice of righthand sides that allows the three lines to intersect at the same point?

ANSWER:

Step 1 of 3

First sketch the given system of equations.

Clearly, from the graph, there is no solution for the given system of equations since the three lines do not intersect at a common point.

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