Question

HELP ME. ISTG

Consider the following set of equations:

Equation A: y = −x + 5
Equation B: y = 6x − 2

Which of the following is a step that can be used to find the solution to the set of equations? (4 points)

−x = 6x + 2
−x − 2 = 6x + 5
−x + 5 = 6x − 2
−x + 5 = 5x


WRONG ANSWER WILL BE REPORTED!.

Answer 1

The answer is:

C. -x + 5 = 6x - 2

Work/explanation:

To solve this system of equations, we will use substitution.

`\begin{cases}\sf{y=-x+5}\\\sf{y=6x-2}\end{cases}}`

Plug -x + 5 for y in the second equation

`\sf{-x+5=6x-2}`

Hence, the answer is C.

Answer 2

-x + 5 = 6x - 2

Explanation:

We have been given two equations and asked to figure out which of the given options is a step that can be used to find the solution to the set of equations.

The given equations are:

`y = -x + 5`

`y = 6x - 2`

As we can see, both equations start with "y = ", meaning anything that follows is equal to y. Therefore, both -x + 5 and 6x -2 are equal to y.

And since y = y,

`-x + 5=6x-2` .

Therefore, the third option is the correct one.

P.S.

If we want to actually solve the given set of equations, we can do so by first solving for x:

`-x + 5=6x-2`

⇒
`-x - 6x + 5= -2` [Subtracting 6x from both sides]

⇒
`-7x + 5=-2`

⇒
`-7x = -2 - 5` [Subtracting from both sides of the equation]

⇒
`-7x =-7`

⇒
`x = (-7)/(-7)` [Dividing both sides by -7]

⇒
`x = \bf 1`

Now we can substitute x = 7 into any of the given equations to get the value of y:

`y = -x + 5`

⇒
`y = -1+5`

⇒
`y = \bf 4`