To determine the correct value of [tex]\( y \)[/tex] that satisfies the equation [tex]\( 6.4x + 2.8y = 44.4 \)[/tex] when [tex]\( x = 3 \)[/tex], we will need to substitute [tex]\( x = 3 \)[/tex] into the equation and calculate the left-hand side for each given value of [tex]\( y \)[/tex].
Given equation:
[tex]\[ 6.4x + 2.8y = 44.4 \][/tex]
1. Substitute [tex]\( x = 3 \)[/tex] into the equation:
[tex]\[ 6.4 \times 3 + 2.8y = 44.4 \][/tex]
2. Calculate the left-hand side for each value of [tex]\( y \)[/tex]:
- For [tex]\( y = 5 \)[/tex]:
[tex]\[ 6.4 \times 3 + 2.8 \times 5 = 19.2 + 14 = 33.2 \][/tex]
- The left-hand side is [tex]\( 33.2 \)[/tex], which does not equal [tex]\( 44.4 \)[/tex].
- For [tex]\( y = 6 \)[/tex]:
[tex]\[ 6.4 \times 3 + 2.8 \times 6 = 19.2 + 16.8 = 36.0 \][/tex]
- The left-hand side is [tex]\( 36.0 \)[/tex], which does not equal [tex]\( 44.4 \)[/tex].
- For [tex]\( y = 8 \)[/tex]:
[tex]\[ 6.4 \times 3 + 2.8 \times 8 = 19.2 + 22.4 = 41.6 \][/tex]
- The left-hand side is [tex]\( 41.6 \)[/tex], which does not equal [tex]\( 44.4 \)[/tex].
- For [tex]\( y = 9 \)[/tex]:
[tex]\[ 6.4 \times 3 + 2.8 \times 9 = 19.2 + 25.2 = 44.4 \][/tex]
- The left-hand side is [tex]\( 44.4 \)[/tex], which equals [tex]\( 44.4 \)[/tex].
3. Conclusion:
The value of [tex]\( y \)[/tex] that satisfies the equation [tex]\( 6.4x + 2.8y = 44.4 \)[/tex] when [tex]\( x = 3 \)[/tex] is:
[tex]\[ y = 9 \][/tex]
