Question

Please Help

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

when using substation you should start with 2(y2-1) - y =4

Answer 2

\[\huge \tt \color{blue}{x = y^2 - 1}\]
\[\huge \tt \color{blue}{2x - y = 4}\]

you know the value of x as \(\large \tt \color{blue}{x = y^2 -1}\) so replace the x in the second equation with that to get:
\[\huge \tt \color{green}{2(y^2 - 1) - y = 4}\]

Answer 3

Use the distributive property and add like terms, if necessary.

Answer 4

\[\huge \tt \color{red}{2y^2 - 2 -y = 4}\]

Answer 5

now move the 4 to the left side by doing the opposite (subtraction property of equality)
\[\huge \tt \color{red}{2y^2 - 2 -y = 4} \rightarrow \huge \tt \color{green}{2y^2 - 6 - y = 0}\]

Answer 6

They put this as a quadratic:
\[\huge \tt \color{purple}{ax^2 + bx + c= 0}\]
We would rearrange this to put it into this format:
\[\huge \tt \color{red}{2y^2 - y - 6 = 0}\]

Answer 7

@Austin1617