Question

x = y^2 - 1
2x - y = 4
Which of the following equations could be the result of using substitution to solve the system?
2y 2 - y - 5 = 0
2y 2 - y - 6 = 0
2y 2 - 2y - 5 = 0

Answer 1

Answer:  The correct option is (B) $2y^2-y-6=0.$

Step-by-step explanation:  We are given the following system of equations :

$x=y^2-1~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\2x-y=4~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

We are to find the equation that could be the result of using substitution to solve the above system.

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

$2x-y=4\\\\\Rightarrow 2(y^2-1)-y=4\\\\\Rightarrow 2y^2-2-y=4\\\\\Rightarrow 2y^2-y-2-4=0\\\\\Rightarrow 2y^2-y-6=0.$

Thus, the required equation is $2y^2-y-6=0.$

Option (B) is CORRECT.