Question

In the system of equations: 3x+3y=−6 and −3x−3y=6. Does the point (2,−4) lie on both of the lines in the system of equations by substituting the ordered pair?

A) Yes
B) No

Answer 1

After substituting the point (2, -4) into both equations (3x + 3y = -6 and -3x - 3y = 6), we find that the point satisfies each equation respectively. Therefore, the point lies on both lines of the system of equations.

Step-by-step explanation:

To determine if the point (2, -4) lies on both lines represented by the equations 3x + 3y = -6 and -3x - 3y = 6, we can substitute the x and y values from the point into each equation.

Substituting into the first equation:

1. 3(2) + 3(-4) = 6 - 12 = -6, which matches the right side of the equation.

Substituting into the second equation:

1. -3(2) - 3(-4) = -6 + 12 = 6, which also matches the right side of the equation.

Since the point satisfies both equations, the answer is Yes, the point (2, -4) does lie on both of the lines in the system of equations.