Questions: Decide which of the ordered pairs are solutions for the equation (y=3 x-2). (0,-2) solution not a solution

Transcript text: Decide which of the ordered pairs are solutions for the equation $y=3 x-2$. $(0,-2)$ $\square$ solution not a solution

Solution

Solution Steps

To determine if an ordered pair is a solution to the equation $ y = 3x - 2 $, substitute the $ x $ and $ y $ values from the ordered pair into the equation. If both sides of the equation are equal, then the ordered pair is a solution; otherwise, it is not.

Solution Approach

Substitute $ x = 0 $ and $ y = -2 $ into the equation $ y = 3x - 2 $.
Check if the left-hand side equals the right-hand side.

Step 1: Substitute Values

We are given the ordered pair $ (0, -2) $. We will substitute $ x = 0 $ and $ y = -2 $ into the equation $ y = 3x - 2 $.

Step 2: Evaluate the Right-Hand Side

Substituting $ x = 0 $ into the equation: \[ y = 3(0) - 2 = 0 - 2 = -2 \]

Step 3: Compare Both Sides

Now we compare the left-hand side $ y = -2 $ with the right-hand side we calculated: \[ -2 = -2 \] Since both sides are equal, the ordered pair $ (0, -2) $ satisfies the equation.