To solve for the missing [tex]\(x\)[/tex] and [tex]\(y\)[/tex] values in the ordered pairs [tex]\((4, y)\)[/tex] and [tex]\((x, 1)\)[/tex], given the equation [tex]\(y = 2x - 3\)[/tex], follow these steps:
### Step 1: Solve for [tex]\(y\)[/tex] when [tex]\(x = 4\)[/tex]
Given [tex]\(x = 4\)[/tex] in the equation [tex]\(y = 2x - 3\)[/tex]:
1. Substitute [tex]\(x = 4\)[/tex] into the equation:
[tex]\[ y = 2(4) - 3 \][/tex]
2. Perform the multiplication:
[tex]\[ y = 8 - 3 \][/tex]
3. Simplify the equation:
[tex]\[ y = 5 \][/tex]
So, the ordered pair is [tex]\((4, 5)\)[/tex].
### Step 2: Solve for [tex]\(x\)[/tex] when [tex]\(y = 1\)[/tex]
Given [tex]\(y = 1\)[/tex] in the equation [tex]\(y = 2x - 3\)[/tex]:
1. Substitute [tex]\(y = 1\)[/tex] into the equation:
[tex]\[ 1 = 2x - 3 \][/tex]
2. Solve for [tex]\(x\)[/tex]:
- Add 3 to both sides of the equation:
[tex]\[ 1 + 3 = 2x \][/tex]
[tex]\[ 4 = 2x \][/tex]
- Divide both sides by 2:
[tex]\[ x = \frac{4}{2} \][/tex]
[tex]\[ x = 2 \][/tex]
So, the ordered pair is [tex]\((2, 1)\)[/tex].
### Summary of Results
The ordered pair [tex]\((4, y)\)[/tex] satisfies the equation with [tex]\(y = 5\)[/tex], giving the pair [tex]\((4, 5)\)[/tex].
The ordered pair [tex]\((x, 1)\)[/tex] satisfies the equation with [tex]\(x = 2\)[/tex], giving the pair [tex]\((2, 1)\)[/tex].
Thus, the missing values are determined to be:
- For [tex]\((4, y)\)[/tex], [tex]\(y = 5\)[/tex].
- For [tex]\((x, 1)\)[/tex], [tex]\(x = 2\)[/tex].
