Question

(08.03)A set of equations is given below:

Equation H: y = −x + 2
Equation J: y = 3x − 4

Which of the following steps can be used to find the solution to the set of equations?
−x = 3x − 4
−x +2 = 3x
−x + 2 = 3x − 4
−x + 1 = 3x + 2

Answer 1

Answer: Third option

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

Explanation:

One of the ways of solving a system of equations is by equating the equations and solving for one of the variables.

In this case we have the system:

`y = -x + 2\\\\y = 3x - 4`

Note that if
`y` is equal
`-x + 2` and also
`y` equals
`3x - 4`

Then logically
`-x + 2` must be equal to
`3x - 4`.

We write equality.

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

Then the correct answer is the third option.

We can also solve for the variable x

`-4x = -6\\\\4x = 6\\\\x = (6)/(4)\\\\x = (3)/(2)`