Question

Which is true regarding the system of equations?

x minus 4 y = 1. 5 x minus 20 y = 4.

Answer 1

No solution

Explanation:

x - 4y = 1 --> (1)

5x - 20y = 4 --> (2)

y = (¼)x - ¼ --> (1)

y = (¼)x - ⅕ --> (2)

Since these are 2 parallel lines with different y-intercepts, they will never meet

Answer 2

Explanation:

`x - 4y = 1.5 \: \: \: \: ...(1) \\ x - 20y = 4 \: \: \: \: ...(2)`

from equation (2) we get,

`x = 20y + 4`

now put the value of x = 20y + 4 in equation (1)

`20y + 4 - 4y = 1.5 \\ 16y = 1.5 - 4 \\ 16y = - 2.5 \\ y = - (25)/(16 * 10) \\ \\ y = - (5)/(32)`

now put the value of y in equation (2) we get

`x - 20( - (5)/(32) ) = 4 \\ \\ x + (100)/(32) = 4 \\ \\ x + (25)/(8) = 4 \\ \\ x = 4 - (25)/(8) \\ \\ x = (32 - 25)/(8) \\ \\ x = (7)/(8)`