Which of the following combined with the equation −9x + 3y = 12 creates a system of linear equations with no solution? select one: a. 18x - 6y = 20 b. 3x - y = -4 c. -16x + 9y = 30 d. 5x + 8y = -1

ANSWER

The correct answer is option A

EXPLANATION

A line that will create a system of equation with no solution when combined with

,is the line that has the same slope as

but different y-intercept.

So, let us write the given equation in slope intercept form to obtain,





The slope is

and y-intercept is


Now let us determine the slope and intercept for the given options too.

For option A,







This has the same slope as the given equation but different y-intercept. When combined with the given equation, there will be no solution, since the two lines will never intersect. so it is the correct option.

For option B,







This option has the same slope and y-intercept as the given line so when combined with this equation, there will be infinitely many solution.

As for option C and D they do not have the same slope as the given line so there will be a unique solution when each is combined with the given line.