Answer :
To determine which ordered pair is a solution to the equation:
[tex]\[ -4x + 7 = 2y - 3, \][/tex]
we will substitute the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] from each ordered pair into the equation and check if the equality holds.
### Step 1: Test the pair [tex]\((2, 1)\)[/tex].
Substitute [tex]\(x = 2\)[/tex] and [tex]\(y = 1\)[/tex] into the equation:
[tex]\[ -4(2) + 7 = 2(1) - 3. \][/tex]
Now compute each side of the equation:
[tex]\[ -4 \cdot 2 + 7 = -8 + 7 = -1, \][/tex]
[tex]\[ 2 \cdot 1 - 3 = 2 - 3 = -1. \][/tex]
Since [tex]\(-1 = -1\)[/tex], the pair [tex]\((2, 1)\)[/tex] satisfies the equation.
### Step 2: Test the pair [tex]\((5, -5)\)[/tex].
Substitute [tex]\(x = 5\)[/tex] and [tex]\(y = -5\)[/tex] into the equation:
[tex]\[ -4(5) + 7 = 2(-5) - 3. \][/tex]
Now compute each side of the equation:
[tex]\[ -4 \cdot 5 + 7 = -20 + 7 = -13, \][/tex]
[tex]\[ 2 \cdot (-5) - 3 = -10 - 3 = -13. \][/tex]
Since [tex]\(-13 = -13\)[/tex], the pair [tex]\((5, -5)\)[/tex] also satisfies the equation.
### Conclusion:
Both ordered pairs, [tex]\((2, 1)\)[/tex] and [tex]\((5, -5)\)[/tex], are solutions of the equation. Therefore, the correct answer is:
[tex]\[ \boxed{\text{Both } (2,1) \text{ and } (5,-5)} \][/tex]
So, the answer is (C) Both [tex]\((2,1)\)[/tex] and [tex]\((5,-5)\)[/tex].
[tex]\[ -4x + 7 = 2y - 3, \][/tex]
we will substitute the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] from each ordered pair into the equation and check if the equality holds.
### Step 1: Test the pair [tex]\((2, 1)\)[/tex].
Substitute [tex]\(x = 2\)[/tex] and [tex]\(y = 1\)[/tex] into the equation:
[tex]\[ -4(2) + 7 = 2(1) - 3. \][/tex]
Now compute each side of the equation:
[tex]\[ -4 \cdot 2 + 7 = -8 + 7 = -1, \][/tex]
[tex]\[ 2 \cdot 1 - 3 = 2 - 3 = -1. \][/tex]
Since [tex]\(-1 = -1\)[/tex], the pair [tex]\((2, 1)\)[/tex] satisfies the equation.
### Step 2: Test the pair [tex]\((5, -5)\)[/tex].
Substitute [tex]\(x = 5\)[/tex] and [tex]\(y = -5\)[/tex] into the equation:
[tex]\[ -4(5) + 7 = 2(-5) - 3. \][/tex]
Now compute each side of the equation:
[tex]\[ -4 \cdot 5 + 7 = -20 + 7 = -13, \][/tex]
[tex]\[ 2 \cdot (-5) - 3 = -10 - 3 = -13. \][/tex]
Since [tex]\(-13 = -13\)[/tex], the pair [tex]\((5, -5)\)[/tex] also satisfies the equation.
### Conclusion:
Both ordered pairs, [tex]\((2, 1)\)[/tex] and [tex]\((5, -5)\)[/tex], are solutions of the equation. Therefore, the correct answer is:
[tex]\[ \boxed{\text{Both } (2,1) \text{ and } (5,-5)} \][/tex]
So, the answer is (C) Both [tex]\((2,1)\)[/tex] and [tex]\((5,-5)\)[/tex].
