Question

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 1

ANSWER

The correct answer is option A

EXPLANATION

A line that will create a system of equation with no solution when combined with
$- 9x + 3y = 12$
,is the line that has the same slope as
$- 9x + 3y = 12$
but different y-intercept.

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

$3y = 9x + 12$

$\Rightarrow \: y = 3x + 4$

The slope is
$3$
and y-intercept is
$4.$

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

For option A,

$18x - 6y = 20$

$\Rightarrow \: - 6y = - 18x + 20$

$\Rightarrow \: y = 3x - \frac{10}{3}$

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,

$3x - y = - 4$

$\Rightarrow \: -y = - 3x - 4$

$\Rightarrow \: y = 3x + 4$

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.