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.