Consider the equation and the following ordered pairs: [tex]$(-2, y)$[/tex] and [tex]$(x, 2)$[/tex].

[tex]\[ y = -2x + 4 \][/tex]

Compute the missing [tex]$x$[/tex] and [tex]$y$[/tex] values so that each ordered pair will satisfy the given equation.



Answer :

Let's solve the problem step by step.

Step 1: Finding the missing [tex]\( y \)[/tex] when [tex]\( x = -2 \)[/tex]

We are given the equation [tex]\( y = -2x + 4 \)[/tex] and need to find the value of [tex]\( y \)[/tex] when [tex]\( x = -2 \)[/tex].

Substitute [tex]\( x = -2 \)[/tex] into the equation:
[tex]\[ y = -2(-2) + 4 \][/tex]

Calculate the value:
[tex]\[ y = 4 + 4 = 8 \][/tex]

So, the ordered pair becomes [tex]\( (-2, 8) \)[/tex].

Step 2: Finding the missing [tex]\( x \)[/tex] when [tex]\( y = 2 \)[/tex]

We are given the equation [tex]\( y = -2x + 4 \)[/tex] and need to find the value of [tex]\( x \)[/tex] when [tex]\( y = 2 \)[/tex].

Substitute [tex]\( y = 2 \)[/tex] into the equation:
[tex]\[ 2 = -2x + 4 \][/tex]

To isolate [tex]\( x \)[/tex], rearrange the equation:
[tex]\[ 2 - 4 = -2x \][/tex]

This simplifies to:
[tex]\[ -2 = -2x \][/tex]

Divide both sides by [tex]\(-2\)[/tex]:
[tex]\[ x = 1 \][/tex]

So, the ordered pair becomes [tex]\( (1, 2) \)[/tex].

Therefore, the missing values are:
- [tex]\( y = 8 \)[/tex] when [tex]\( x = -2 \)[/tex]
- [tex]\( x = 1 \)[/tex] when [tex]\( y = 2 \)[/tex]

Thus, the ordered pairs that satisfy the equation [tex]\( y = -2x + 4 \)[/tex] are [tex]\( (-2, 8) \)[/tex] and [tex]\( (1, 2) \)[/tex].