Question

What is the result of substituting for y in the bottom equation? y = x – 3 y = x2 + 2x – 4 A. (x – 3) = x2 B. y = (x – 3)2 + 2(x – 3) – 4 C. x – 3 = x2 + 2x – 4 D. y = x2 + 2x – 4 – (x – 3)

Answer 1

C.
`x-3=x^2+2x-4`

Explanation:

We are given that two equations

`y=x-3` ....(1)

`y=x^2+2x-4`....(2)

We have to find the result of substituting for y in given equations.

To find the result of substituting for y we will substitute the value of y in any one equation .

Substitute the value of y in equation (2)

Then, we get

`x-3=x^2+2x-4`

Hence, this is the result of substituting for y in given equation.

Hence, option C is true.

C.
`x-3=x^2+2x-4`

Answer 2

We have been given two equations.

`y=x-3` and
`y=x^(2)+2x-4`

When we will substitute y in one of these equation we will get

`x-3=x^(2)+2x-4`

Now let us find which of the given options are equivalent to our equation.

A)
`x-3=x^(2)` This is not equivalent to our answer.
`2x-4` is missing.

B)
`y=(x-3)^(2)+2(x-3)-4` In this equation y's value has been substituted in place of x which will make the equation wrong. When we will substitute value of
`x-3` we will get
`y=(y)^(2)+2(y)-4` which is not true.

C)
`x-3=x^(2)+2x-4` is equivalent to our equation.

D)
`y=x^(2)+2x-4-(x-3)` In this equation
`x-3` is being subtracted from
`x^(2)+2x-4`. When we will simlify this equation we will get

`y=x^(2)+2x-4+x+3=x^(2)+3x-1` This is not true and we were asked only to substitute y in our given equation.

Therefore option C is correct.