Sure! Let's find the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is equal to -7 in the equation:
[tex]\[ -7x - 5y = 54 \][/tex]
### Step-by-Step Solution:
1. Substitute [tex]\( x = -7 \)[/tex] into the equation:
[tex]\[ -7(-7) - 5y = 54 \][/tex]
2. Simplify the substituted value:
[tex]\[ 49 - 5y = 54 \][/tex]
3. Re-arrange the equation to isolate the term with [tex]\( y \)[/tex]:
[tex]\[ 49 - 54 = 5y \][/tex]
4. Simplify the difference:
[tex]\[ -5 = 5y \][/tex]
5. Solve for [tex]\( y \)[/tex] by dividing both sides by 5:
[tex]\[ y = \frac{-5}{5} \][/tex]
[tex]\[ y = -1 \][/tex]
### Conclusion:
The value of [tex]\( y \)[/tex] when [tex]\( x = -7 \)[/tex] is:
[tex]\[ y = -1 \][/tex]
Thus, substituting [tex]\( x = -7 \)[/tex] into the original equation [tex]\( -7x - 5y = 54 \)[/tex] gives us [tex]\( y = -1 \)[/tex].
