Sure, let's solve the problem step by step to find the values for [tex]\( x \)[/tex] and [tex]\( y \)[/tex] that will balance the hanger.
We have the following system of equations based on the given information:
1. [tex]\( 2x + 3 = y \)[/tex]
2. [tex]\( x = 3 \)[/tex]
From the second equation, we know that [tex]\( x \)[/tex] is equal to 3.
Now, let's substitute [tex]\( x = 3 \)[/tex] into the first equation:
[tex]\[ 2(3) + 3 = y \][/tex]
Simplify the left-hand side of the equation:
[tex]\[ 6 + 3 = y \][/tex]
So,
[tex]\[ y = 9 \][/tex]
Therefore, the values that balance the hanger are:
[tex]\[ x = 3 \][/tex]
[tex]\[ y = 9 \][/tex]
So the hanger will balance with [tex]\( x = 3 \)[/tex] lbs and [tex]\( y = 9 \)[/tex] lbs.
