Answer :
Certainly! Let's find the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] by comparing the given ordered pairs step-by-step.
### Step (a)
Given:
[tex]\[ (4, y) = (x, 7) \][/tex]
To find [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
1. Compare the first elements:
[tex]\[ 4 = x \][/tex]
So, [tex]\( x = 4 \)[/tex].
2. Compare the second elements:
[tex]\[ y = 7 \][/tex]
So, [tex]\( y = 7 \)[/tex].
From step (a), we determined that:
[tex]\[ x = 4, \quad y = 7 \][/tex]
### Step (b)
Given:
[tex]\[ (6, y) = (x, 5) \][/tex]
To find [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
1. Compare the first elements:
[tex]\[ 6 = x \][/tex]
So, [tex]\( x = 6 \)[/tex].
2. Compare the second elements:
[tex]\[ y = 5 \][/tex]
So, [tex]\( y = 5 \)[/tex].
From step (b), we determined that:
[tex]\[ x = 6, \quad y = 5 \][/tex]
### Step (c)
Given:
[tex]\[ (2, 3) = (x-1, y) \][/tex]
To find [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
1. Compare the first elements:
[tex]\[ 2 = x - 1 \][/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[ 2 + 1 = x \implies x = 3 \][/tex]
2. Compare the second elements:
[tex]\[ 3 = y \][/tex]
So, [tex]\( y = 3 \)[/tex].
From step (c), we determined that:
[tex]\[ x = 3, \quad y = 3 \][/tex]
### Summary of Solutions
Thus, the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] for all given pairs are:
- From (a): [tex]\( x = 4, y = 7 \)[/tex]
- From (b): [tex]\( x = 6, y = 5 \)[/tex]
- From (c): [tex]\( x = 3, y = 3 \)[/tex]
Putting it all together, the solutions for the ordered pairs are:
[tex]\[ \begin{cases} (x, y) &= (4, 7) \\ (x, y) &= (6, 5) \\ (x - 1, y) &= (2, 3) \text{ which gives } (x, y) = (3, 3) \end{cases} \][/tex]
### Step (a)
Given:
[tex]\[ (4, y) = (x, 7) \][/tex]
To find [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
1. Compare the first elements:
[tex]\[ 4 = x \][/tex]
So, [tex]\( x = 4 \)[/tex].
2. Compare the second elements:
[tex]\[ y = 7 \][/tex]
So, [tex]\( y = 7 \)[/tex].
From step (a), we determined that:
[tex]\[ x = 4, \quad y = 7 \][/tex]
### Step (b)
Given:
[tex]\[ (6, y) = (x, 5) \][/tex]
To find [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
1. Compare the first elements:
[tex]\[ 6 = x \][/tex]
So, [tex]\( x = 6 \)[/tex].
2. Compare the second elements:
[tex]\[ y = 5 \][/tex]
So, [tex]\( y = 5 \)[/tex].
From step (b), we determined that:
[tex]\[ x = 6, \quad y = 5 \][/tex]
### Step (c)
Given:
[tex]\[ (2, 3) = (x-1, y) \][/tex]
To find [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
1. Compare the first elements:
[tex]\[ 2 = x - 1 \][/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[ 2 + 1 = x \implies x = 3 \][/tex]
2. Compare the second elements:
[tex]\[ 3 = y \][/tex]
So, [tex]\( y = 3 \)[/tex].
From step (c), we determined that:
[tex]\[ x = 3, \quad y = 3 \][/tex]
### Summary of Solutions
Thus, the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] for all given pairs are:
- From (a): [tex]\( x = 4, y = 7 \)[/tex]
- From (b): [tex]\( x = 6, y = 5 \)[/tex]
- From (c): [tex]\( x = 3, y = 3 \)[/tex]
Putting it all together, the solutions for the ordered pairs are:
[tex]\[ \begin{cases} (x, y) &= (4, 7) \\ (x, y) &= (6, 5) \\ (x - 1, y) &= (2, 3) \text{ which gives } (x, y) = (3, 3) \end{cases} \][/tex]
