Question

How many points of intersection will the following system of linear equations have? y = 9x, 3y = -3x - 5 a) 0 b) 1 c) 2 d) Infinite

Answer 1

b

Explanation:

given the system of equations

y = 9x → (1)

3y = - 3x - 5 → (2)

substitute y = 9x into (2)

3(9x) = - 3x - 5

27x = - 3x - 5 ( add 3x to both sides )

30x = - 5 (divide both sides by 30 )

x = -
`(5)/(30)` = -
`(1)/(6)`

substitute x = -
`(1)/(6)` into (1) and solve for y

y = 9x = 9 × -
`(1)/(6)` = -
`(9)/(6)` = -
`(3)/(2)`

point of intersection = ( -
`(1)/(6)`, -
`(3)/(2)` )