To find the value of [tex]\( y \)[/tex] that completes the ordered pair [tex]\((6, y)\)[/tex] so that it satisfies the equation [tex]\( 3x + 2y = 36 \)[/tex], we can follow these steps:
1. Substitute [tex]\( x \)[/tex] with 6:
Since the given x-value is 6, we replace [tex]\( x \)[/tex] in the equation with 6. The equation then becomes:
[tex]\[
3(6) + 2y = 36
\][/tex]
2. Simplify the equation:
Calculate [tex]\( 3 \times 6 \)[/tex]:
[tex]\[
18 + 2y = 36
\][/tex]
3. Isolate [tex]\( 2y \)[/tex]:
Subtract 18 from both sides of the equation to isolate [tex]\( 2y \)[/tex]:
[tex]\[
2y = 36 - 18
\][/tex]
Simplify the right side:
[tex]\[
2y = 18
\][/tex]
4. Solve for [tex]\( y \)[/tex]:
Divide both sides of the equation by 2 to solve for [tex]\( y \)[/tex]:
[tex]\[
y = \frac{18}{2}
\][/tex]
Simplify the division:
[tex]\[
y = 9
\][/tex]
The ordered pair that satisfies the equation [tex]\( 3x + 2y = 36 \)[/tex] with [tex]\( x = 6 \)[/tex] is [tex]\((6, 9)\)[/tex].
So, the correct option is:
[tex]\[
(6, 9)
\][/tex]
