Question

The graph for the equation y=-2x+1 is shown below. If another equation is graphed so that the system has no solution, which equation could that be?

Answer 1

Answer:

c

Step-by-step explanation:

Answer 2

Given:

Equation: y = -2x + 1

To Find:

Another equation from the given options so that the system has no solution

Solution:

For a system of linear equations to have no solutions, the graph of each of the equations should never intersect.  

Evaluating y = - 2 ( x - 1/2)

Opening the brackets,

y = - 2x + 1  

This is the same equation as in the question, hence the graphs will be coinciding and this system will have infinite solutions.

Evaluationg y = - 1/2 ( 4x + 2)  

y = - 2x - 1

If we take x = 0, then  

y = - 2 ( 0)  - 1= - 1  

Now taking x = 1 and solving, we get y = -3

⇒ (0, -1) and ( 1, -3) are solutions to this equation.

The plotted graph (red) is parallel to the given graph.

(Green and purple graphs show equations c an d respectively.)

Hence, (b) y = - 1/2 ( 4x + 2) is the required equation.