Question

How many solutions does this linear system have?

Answer 1

second option

Explanation:

Given the 2 equations

y =
`(2)/(3)` x + 2 → (1)

6x - 4y = - 10 → (2)

Substitute y =
`(2)/(3)` x + 2 into (2)

6x - 4(
`(2)/(3)` x + 2) = - 10 ← distribute parenthesis and simplify left side

6x -
`(8)/(3)` x - 8 = - 10 ( multiply through by 3 to clear the fraction )

18x - 8x - 24 = - 30

10x - 24 = - 30 ( add 24 to both sides )

10x = - 6 ( divide both sides by 10 )

x = - 0.6

Substitute x = - 0.6 into (1) and evaluate for y

y =
`(2)/(3)` × - 0.6 + 2 = 2x × - 0.2 + 2 = - 0.4 + 2 = 1.6

One Solution is (- 0.6, 1. 6 )