Answer: The correct option is (B) (1, -2).
Step-by-step explanation: We are given to solve the following system of equations by substitution method :
[tex]y=2x^2-3x-1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y=x-3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Substituting the value of y from equation (ii) in equation (i), we get
[tex]x-3=2x^2-3x-1\\\\\Rightarrow 2x^2-4x+2=0\\\\\Rightarrow x^2-2x+1=0\\\\\Rightarrow (x-1)^2=0\\\\\Rightarrow x-1=0,~~~x-1=0\\\\\Rightarrow x=1,1.[/tex]
Substituting x = 1 in equation (ii), we get
[tex]y=1-3=-2.[/tex]
Thus, the required solution is (x, y) = (1, -2).
Option (B) is correct.
