Question

Which of the following is a solution to the system shown below? y = 3x 2 - 8x - 2 and 2x - y = 5 (1, 3) (1/3,-13/3) (-1/3,13/3) (17/6, 0)

Answer 1

y=3x^2-8x-2 and 2x-y=5
your answer is (1/3,-13/3

good luck

Answer 2

Option B

Explanation:

We have to find the solution to the system of equations

y = 3x² - 8x - 2 ----------------(1)

2x - y = 5

y = 2x - 5 -----------------(2)

Now equate the equations (1) and (2) for the values of y.

3x² - 8x - 2 = 2x - 5

3x² - 8x - 2x - 2 + 5 = 0

3x² - 10x + 3 = 0

3x² - 9x - x + 3 = 0

3x ( x-3 ) - 1 ( x-3 ) = 0

( 3x - 1 ) ( x-3 ) = 0

x =
`(1)/(3)` and 3

Now we put x =
`(1)/(3)` and 3 in equation (2)

y = 2 ×
`((1)/(3))` - 5

=
`(2-15)/(3)` =
`(-13)/(3)`

and y = 3 × 2 - 5

= 6 - 5

= 1

So solutions are
`((1)/(3)`,
`(-13)/(3))` and ( 3, 1 )

Option B is the answer.