Answer :
To determine which of the given ordered pairs is a solution to the equation [tex]\( 2x + 7y = 8 \)[/tex], we need to substitute each pair into the equation and check if the equation holds true. Let's evaluate each pair step-by-step.
1. Ordered pair [tex]\((0, 4)\)[/tex]:
[tex]\[ x = 0, \, y = 4 \][/tex]
Substitute [tex]\( x \)[/tex] and [tex]\( y \)[/tex] into the equation:
[tex]\[ 2(0) + 7(4) = 2 \cdot 0 + 7 \cdot 4 = 0 + 28 = 28 \][/tex]
[tex]\( 28 \neq 8 \)[/tex], so [tex]\((0, 4)\)[/tex] is not a solution.
2. Ordered pair [tex]\((-3, 2)\)[/tex]:
[tex]\[ x = -3, \, y = 2 \][/tex]
Substitute [tex]\( x \)[/tex] and [tex]\( y \)[/tex] into the equation:
[tex]\[ 2(-3) + 7(2) = 2 \cdot -3 + 7 \cdot 2 = -6 + 14 = 8 \][/tex]
[tex]\( 8 = 8 \)[/tex], so [tex]\((-3, 2)\)[/tex] is a solution.
3. Ordered pair [tex]\((2, -3)\)[/tex]:
[tex]\[ x = 2, \, y = -3 \][/tex]
Substitute [tex]\( x \)[/tex] and [tex]\( y \)[/tex] into the equation:
[tex]\[ 2(2) + 7(-3) = 2 \cdot 2 + 7 \cdot -3 = 4 - 21 = -17 \][/tex]
[tex]\( -17 \neq 8 \)[/tex], so [tex]\((2, -3)\)[/tex] is not a solution.
4. Ordered pair [tex]\((3, -2)\)[/tex]:
[tex]\[ x = 3, \, y = -2 \][/tex]
Substitute [tex]\( x \)[/tex] and [tex]\( y \)[/tex] into the equation:
[tex]\[ 2(3) + 7(-2) = 2 \cdot 3 + 7 \cdot -2 = 6 - 14 = -8 \][/tex]
[tex]\( -8 \neq 8 \)[/tex], so [tex]\((3, -2)\)[/tex] is not a solution.
After evaluating each pair, the only pair that satisfies the equation [tex]\( 2x + 7y = 8 \)[/tex] is [tex]\((-3, 2)\)[/tex]. Therefore, the ordered pair [tex]\((-3, 2)\)[/tex] is a solution to the equation.
1. Ordered pair [tex]\((0, 4)\)[/tex]:
[tex]\[ x = 0, \, y = 4 \][/tex]
Substitute [tex]\( x \)[/tex] and [tex]\( y \)[/tex] into the equation:
[tex]\[ 2(0) + 7(4) = 2 \cdot 0 + 7 \cdot 4 = 0 + 28 = 28 \][/tex]
[tex]\( 28 \neq 8 \)[/tex], so [tex]\((0, 4)\)[/tex] is not a solution.
2. Ordered pair [tex]\((-3, 2)\)[/tex]:
[tex]\[ x = -3, \, y = 2 \][/tex]
Substitute [tex]\( x \)[/tex] and [tex]\( y \)[/tex] into the equation:
[tex]\[ 2(-3) + 7(2) = 2 \cdot -3 + 7 \cdot 2 = -6 + 14 = 8 \][/tex]
[tex]\( 8 = 8 \)[/tex], so [tex]\((-3, 2)\)[/tex] is a solution.
3. Ordered pair [tex]\((2, -3)\)[/tex]:
[tex]\[ x = 2, \, y = -3 \][/tex]
Substitute [tex]\( x \)[/tex] and [tex]\( y \)[/tex] into the equation:
[tex]\[ 2(2) + 7(-3) = 2 \cdot 2 + 7 \cdot -3 = 4 - 21 = -17 \][/tex]
[tex]\( -17 \neq 8 \)[/tex], so [tex]\((2, -3)\)[/tex] is not a solution.
4. Ordered pair [tex]\((3, -2)\)[/tex]:
[tex]\[ x = 3, \, y = -2 \][/tex]
Substitute [tex]\( x \)[/tex] and [tex]\( y \)[/tex] into the equation:
[tex]\[ 2(3) + 7(-2) = 2 \cdot 3 + 7 \cdot -2 = 6 - 14 = -8 \][/tex]
[tex]\( -8 \neq 8 \)[/tex], so [tex]\((3, -2)\)[/tex] is not a solution.
After evaluating each pair, the only pair that satisfies the equation [tex]\( 2x + 7y = 8 \)[/tex] is [tex]\((-3, 2)\)[/tex]. Therefore, the ordered pair [tex]\((-3, 2)\)[/tex] is a solution to the equation.
