Question

How many solutions does this linear system have?

y = 2/3 x+ 2

6x – 4y = –10

one solution: (–0.6, –1.6)
one solution: (–0.6, 1.6)
no solution
infinite number of solutions

Answer 1

B. one solution: (–0.6, 1.6)

Explanation:

Answer 2

Equation 1:
`y = (2)/(3)x+2`
Equation 2:
`6x-4y=-10`

Substitute Equation 1 into Equation 2


`6x-4[ (2)/(3)x+2]=-10`

`6x- (8)/(3)x -8=-10`

`(10)/(3)x-8=-10`

`(10)/(3)x=-10+8`

`(10)/(3)x=-2`

`10x=-6`

`x=- (6)/(10)`

`x=-0.6`

Substitute x = -0.6 into either Equation 1 or Equation 2 to work out 'y'


`y= (2)/(3)(-0.6)+2 = 1.6`

The linear system only have one solution (-0.6, 1.6)

Correct answer: B