Question

Solve for each system of equations by substitution or elimination.

Answer 1

QUESTION 1

The given system of equations are:

$y=x^2+5x+1$

$y=x^2+2x+1$

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.