Question

Solve the following system.

y = -2x^2 + 3x - 1 and x + y = -1.

The solutions are
and

Answer 1

Given:

The equations of a system of equations are

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

`x+y=-1`

To find:

The solution of the given system of equations.

Solution:

We have,

`y=-2x^2+3x-1` ...(i)

`x+y=-1` ...(ii)

Using (i) and (ii), we get

`x+(-2x^2+3x-1)=-1`

`x-2x^2+3x-1+1=0`

`-2x^2+4x=0`

Taking out the common factors.

`2x(-x+2)=0`

Using zero product property,we get

`2x=0` and
`-x+2=0`

`x=0` and
`2=x`

For x=0, we have

`0+y=-1`

`y=-1`

For x=2, we have

`2+y=-1`

`y=-1-2`

`y=-3`

Therefore, the two solutions of the given system of equations are (0,-1) and (2,-3).