To find the missing coordinates for the given ordered-pairs given the linear equation:
[tex]\[ 2x - 3y = -6 \][/tex]
### Part (a) [tex]\((3, \_)\)[/tex]
We need to find the y-coordinate when [tex]\( x = 3 \)[/tex].
1. Substitute [tex]\( x = 3 \)[/tex] into the equation:
[tex]\[ 2(3) - 3y = -6 \][/tex]
[tex]\[ 6 - 3y = -6 \][/tex]
2. Solve for [tex]\( y \)[/tex]:
[tex]\[ 6 - 6 = 3y \][/tex]
[tex]\[ 12 = 3y \][/tex]
[tex]\[ y = \frac{12}{3} \][/tex]
[tex]\[ y = 4 \][/tex]
So, the complete ordered-pair for (a) is [tex]\((3, 4)\)[/tex].
### Part (b) [tex]\((\_, -4)\)[/tex]
We need to find the x-coordinate when [tex]\( y = -4 \)[/tex].
1. Substitute [tex]\( y = -4 \)[/tex] into the equation:
[tex]\[ 2x - 3(-4) = -6 \][/tex]
[tex]\[ 2x + 12 = -6 \][/tex]
2. Solve for [tex]\( x \)[/tex]:
[tex]\[ 2x = -6 - 12 \][/tex]
[tex]\[ 2x = -18 \][/tex]
[tex]\[ x = \frac{-18}{2} \][/tex]
[tex]\[ x = -9 \][/tex]
So, the complete ordered-pair for (b) is [tex]\((-9, -4)\)[/tex].
### Part (c) [tex]\((\_, 5)\)[/tex]
We need to find the x-coordinate when [tex]\( y = 5 \)[/tex].
1. Substitute [tex]\( y = 5 \)[/tex] into the equation:
[tex]\[ 2x - 3(5) = -6 \][/tex]
[tex]\[ 2x - 15 = -6 \][/tex]
2. Solve for [tex]\( x \)[/tex]:
[tex]\[ 2x = -6 + 15 \][/tex]
[tex]\[ 2x = 9 \][/tex]
[tex]\[ x = \frac{9}{2} \][/tex]
[tex]\[ x = 4.5 \][/tex]
So, the complete ordered-pair for (c) is [tex]\((4.5, 5)\)[/tex].
### Summary of Results:
(a) [tex]\((3, 4)\)[/tex]
(b) [tex]\((-9, -4)\)[/tex]
(c) [tex]\((4.5, 5)\)[/tex]
