Question

Mathe question 2 help

Answer 1

Option B

See below

Explanation:

Two simultaneous equations:

`7x - 4y - 8 = 0` —————- (equation i)

`2x^(2) + x + 4y + 8 = 0` ——- (equation ii)

Step 1:

Rearrange (equation i):

`7x - 4y = 8` ———- updated (equation i)

Step 2:

Substitute the updated (equation i) into (equation ii) and bring like terms together to simplify them in reduced forms:

`2x^(2) + x + 4y + (7x - 4y) = 0`

`2x^(2) + x + 4y + 7x - 4y = 0`

`2x^(2) + x + 7x + 4y - 4y = 0`

`2x^(2) + 8x = 0`

Step 3:

Factorize:

`2x(x + 4) = 0`

Either
`2x = 0`
∴
`x = 0`

Or
`x + 4 = 0`

∴
`x = -4`

Step 4:

Substitute these values of x in (equation ii) to determine their corresponding values of y:

For x = 0:

`2(0)^(2) + 0 + 4y + 8 = 0`

`4y + 8 = 0`

`4y = -8`

`y = (8)/(-4)`

∴
`y = -2`

For x = -4:

`2(-4)^(2) + (-4) +4y + 8 = 0`

`2(16) - 4 + 4y + 8 = 0`

`32 - 4 + 4y + 8 = 0`

`32 - 4 + 8 + 4y = 0`

`36 + 4y = 0`

`4y = -36`

`y = (-36)/(4)`

∴
`y = -9`

∴The values of y are
`-2` and
`-9`

∴Option B