Question

Which statements are true regarding the system of equations?

4x + 5y = 15.
28x + 35y = 105.

a. The lines coincide.
b. The lines are parallel.
c. The slopes are equal.
d. The y-intercepts are different.
e. The y-intercepts are the same.
f. The system has an infinite number of solutions.
g. The system has no solution.
h. The system has one solution.

Answer 1

The system of equations given represents two lines that coincide. They have the same slope and y-intercept, and therefore, the system has an infinite number of solutions.

Step-by-step explanation:

When assessing whether the statements are true regarding the system of equations:

• 4x + 5y = 15
• 28x + 35y = 105

We observe that the second equation is simply the first equation multiplied by 7. This means they have the same slope and y-intercept, as the relationship between 'x' and 'y' has not changed.

Here are the truths about the system:

• The lines coincide.
• The slopes are equal because when the second equation is reduced by dividing all terms by 7, it becomes identical to the first.
• The y-intercepts are the same because both lines cross the y-axis at the same point when the equations are in slope-intercept form (y = mx + b).
• The system has an infinite number of solutions because they represent the same line.

The correct statements are:

• a. The lines coincide.
• c. The slopes are equal.
• e. The y-intercepts are the same.
• f. The system has an infinite number of solutions.