Question

Which statements are true regarding the system of equations? Check all that apply.

8 x + 10 y = 30. 12 x + 15 y = 60.
The lines coincide.
The lines are parallel.
The slopes are equal.
The y-intercepts are different.
The system has one solution.
The system has an infinite number of solutions.
The system has no solution.

Answer 1

The slopes of the lines are equal and the lines are parallel.

Step-by-step explanation:

The given system of equations is:

8x + 10y = 30

12x + 15y = 60

To determine which statements are true regarding this system of equations, we can analyze the slopes and y-intercepts of the lines represented by the equations.

First, let's solve the system of equations:

Multiplying the first equation by 3, we get:

24x + 30y = 90

Subtracting the second equation from this equation, we obtain:

-12x - 15y = -30

Simplifying, we get:

-12x - 15y = -30

The slopes of the lines are equal.

Since the y-intercepts are different, the lines are not coincident.

Since the slopes are equal and the y-intercepts are different, the lines are parallel.

Therefore, the statements that are true regarding the system of equations are: The slopes are equal and the lines are parallel.

Answer 2

• The lines are parallel.
• The slopes are equal.
• The y-intercepts are different.
• The system has no solution.

Step-by-step explanation:

If the first equation is multiplied by 1.5, it will be transformed into the dependent equation

12x +15y = 45

This is different from the second given equation, so that 2nd equation is not dependent upon the first. Rather it is the equation of a line parallel to the first. (See below for a graph.)

The lines are parallel.

The slopes are equal.

The y-intercepts are different.

The system has no solution.