Question

In attempting to solve the system of equations y = 3x - 2 and 6x - 2y = 4, John graphed the two equations on his graphing calculator. Because he saw only one line, John wrote the answer to the system is the empty set. Is he correct? Explain your answer.

Answer 1

Answer:

He is not correct, the answer is All Real Numbers.

Step-by-step explanation:

When two lines are right on top of each other, the solution set is All Real Numbers that are on both lines because the solution set is the point(s) at which the lines overlap.

Answer 2

The solution of both equations is all points on the line, therefore, John is not correct.

Given that,

The system of equations is as follows;

$\rm y=3x-2\\\\6x-2y=4$

According to the question,

To determine the solution of the system of equation following all the steps given below.

Dividing equation 2 by 2,

$\rm 6x-2y=4\\\\3x-y=2\\\\y = 3x-2$

After being divided by 2 the equation becomes the same.

In the case of parallel lines, there are no common points.

Intersecting lines have one point in common and coincident lines have infinitely many points in common.

A two-variable system of equations is considered as equations of two lines and they can have infinitely many solutions if these two lines are parallel where they can be expressed as multiples of each other,

Hence, the solution of both equations is all points on the line, therefore, John is not correct.

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