Question

The lines represented by the equations 25y- 20x=100 and 5y - 4x = 20 are

Answer 1

Answer:

The system of equations represent the same line ⇒ B

Step-by-step explanation:

In the system of equations ax + by = c and dx + ey = f, if

• a = d, b = e, and c = f, then the system of the equations represent the same line

• a = d, b = e, and c ≠ f, then the system of the equations represent two parallel lines

• a ≠ d, and/or b ≠ e, and/or c ≠ f, then the system of the equations represent two intersecting lines

∵ The one line represented by the equation 25y - 20x = 100

→ Divide the terms of the equation by 5 to simplify it

∴ 5y - 4x = 20 ⇒ (1)

∴ a = 5, b = -4, c = 20

∵ The other line represented by the equation 5y - 4x = 20 ⇒ (2)

∴ d = 5, e = -4, f = 20

→ Compare the two equations

∵ a = d, b = e, c = f

→ By using the 1st case above

∴ The system of equations represent the same line