Question

One equation in a system of equations is given in the graph. Which equation below would have to be the second equation so that the system has no solutions?

Answer 1

Solution:

To classify the system of equations as no solutions, the lines must be parallel (Not intersect).

First, let's identify the equation forming the line.

• Slope = Rise/Run = 2/-3 = -0.66
• Y-intercept = 0
• Equation formed: y = -2/3

We also know that the slope of the equation must be -1.5.

A) 2x + 3y = 0

• 3y = 0 - 2x
• => 3y = -2x
• => (y = -2x/3) ∦ (y = -2x/3)

B) 2x + 3y = 6

• => 3y = -2x + 6
• => (y = -2x/3 + 2) ║ (y = -2x/3)

C) 2x - 3y = 9

• => -3y = -2x + 9
• => y = -2x/-3 + 9/-3
• => (y = 2x/3 - 3) ∦ (y = -2x/3)

D) y = 3x + 2

• (y = 3x + 2) ∦ (y = -2x/3)

Option B is correct.