Question

Solve for each system of equations by substitution or elimination.

1.Y=x^2+5x+1

Y=x^2+2x+1


2. Y=x^2-2x-1

Y= -x^2-2x-1


3. Y=x^2+2x+1

Y=x^2+2x-1

Answer 1

QUESTION 1

The given system of equations are:

`y=x^2+5x+1</p><p>`

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

We equate the two equations to get:

`x^2+5x+1 =x^2+2x+1`

`x^2 - {x}^(2) + 5x - 2x = 1 - 1`

`3x = 0`

`x = 0`

When x=0,

`y=0^2+2(0)+1 = 1`

The solution is (0,1)

QUESTION 2

The given equations are:

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

and

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

We equate both equations to get:

`x^2-2x - 1 = -x^2-2x-1`

Group similar terms,

`x^2 + {x}^(2) -2x + 2x= -1 + 1`

`2 {x}^(2) = 0`

`x = 0`

We put x=0 into any of the equations to find y.

`y= -0^2-2(0)-1 = - 1`

The solution is (0,-1).

QUESTION 3

The given equations are:

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

and

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

We equate both equations:

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

Group similar terms:

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

`0 = -2`

This is not true.

Hence the system has no solution.