Question

Solve the system algebraically (Elimination or Substitution).y= x2 - 2y= - 2x + 1

Answer 1

Given data:

The first equation is y=x^2 -2.

The second equation is y=-2x+1.

Substitute the value of y from first equation and put in second equation.

`\begin{gathered} x^2-2=-2x+1 \\ x^2+2x-3=0 \\ x^2+3x-x-3=0 \\ x(x+3)-1(x+3)=0 \\ (x-1)(x+3)=0 \\ x=1,\text{ -3} \end{gathered}`

The values of y is,

`\begin{gathered} y=(1)^2-2 \\ =-1 \\ y=(-3)^2-2 \\ =7 \end{gathered}`

Thus, the values are (1,-1) and (-3,7).