Question

Solve the system by substitution. y=2x^2-3x-1 y=x-3

Answer 1

The answer is B(1,-2). This is the only point where the two lines intercept. & if you plug the numbers into the equations they fit.

Answer 2

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 :

$y=2x^2-3x-1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y=x-3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Substituting the value of y from equation (ii) in equation (i), we get

$x-3=2x^2-3x-1\\\\\Rightarrow 2x^2-4x+2=0\\\\\Rightarrow x^2-2x+1=0\\\\\Rightarrow (x-1)^2=0\\\\\Rightarrow x-1=0,~~~x-1=0\\\\\Rightarrow x=1,1.$

Substituting x = 1 in equation (ii), we get

$y=1-3=-2.$

Thus, the required solution is (x, y) = (1, -2).

Option (B) is correct.