Sure! Let's solve the given linear equation [tex]\( 5x - 6y = 39 \)[/tex] and find the missing coordinates for each part.
### Part (a): Find the missing y-coordinate when [tex]\( x = -3 \)[/tex]
We start with the linear equation:
[tex]\[ 5x - 6y = 39 \][/tex]
Substitute [tex]\( x = -3 \)[/tex] into the equation:
[tex]\[ 5(-3) - 6y = 39 \][/tex]
Simplify the equation:
[tex]\[ -15 - 6y = 39 \][/tex]
Next, we isolate the term with [tex]\( y \)[/tex]:
[tex]\[ -6y = 39 + 15 \][/tex]
[tex]\[ -6y = 54 \][/tex]
Divide both sides by -6 to solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{54}{-6} \][/tex]
[tex]\[ y = -9 \][/tex]
Therefore, the ordered-pair solution is [tex]\( (-3, -9) \)[/tex].
### Part (b): Find the missing x-coordinate when [tex]\( y = 1 \)[/tex]
We start again with the same linear equation:
[tex]\[ 5x - 6y = 39 \][/tex]
Substitute [tex]\( y = 1 \)[/tex] into the equation:
[tex]\[ 5x - 6(1) = 39 \][/tex]
Simplify the equation:
[tex]\[ 5x - 6 = 39 \][/tex]
Next, we isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 5x = 39 + 6 \][/tex]
[tex]\[ 5x = 45 \][/tex]
Divide both sides by 5 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{45}{5} \][/tex]
[tex]\[ x = 9 \][/tex]
Therefore, the ordered-pair solution is [tex]\( (9, 1) \)[/tex].
To summarize:
(a) The ordered-pair solution is [tex]\( (-3, -9) \)[/tex].
(b) The ordered-pair solution is [tex]\( (9, 1) \)[/tex].
