Question

Solve the following system.

y= (3x2+2x-1 and 3x-y=1
The solutions are and
remember to include the commas)

Answer 1

The solutions are:

`(0, -1)\ and\ ((1)/(3), 0)`

Solution:

Given that,

`y = 3x^2 + 2x-1-------- eqn 1\\\\\3x-y=1 ------- eqn 2`

From eqn 2,

3x - y = 1

y = 3x - 1

Substitute the above in eqn 1

`3x -1 = 3x^2 + 2x - 1\\\\3x^2 + 2x - 3x =0\\\\3x^2 -x = 0\\\\x(3x - 1) = 0\\\\Therefore,\\\\x = 0\\\\And\\\\3x - 1 = 0\\\\3x = 1\\\\x = (1)/(3)`

When, x = 0

Substitute x = 0 in eqn 2

3(0) - y = 1

y = -1

When x = 1/3

Substitute x = 1/3 in eqn 2

`3(1)/(3) - y = 1\\\\ 1 - y = 1\\\\y = 0`

Thus solutions are:

`(0, -1)\ and\ ((1)/(3), 0)`