Let's solve the given system of equations step-by-step to find the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
The system of equations is:
1. [tex]\( x + y = 29 \)[/tex]
2. [tex]\( x + 8 = 2(y + 8) \)[/tex]
We are also given that [tex]\( y = 5 \)[/tex].
First, substitute [tex]\( y = 5 \)[/tex] into the first equation:
1. [tex]\( x + 5 = 29 \)[/tex]
To solve for [tex]\( x \)[/tex], subtract 5 from both sides:
[tex]\[ x = 29 - 5 \][/tex]
[tex]\[ x = 24 \][/tex]
So from the first equation, [tex]\( x = 24 \)[/tex] when [tex]\( y = 5 \)[/tex].
Next, substitute [tex]\( y = 5 \)[/tex] into the second equation:
2. [tex]\( x + 8 = 2(5 + 8) \)[/tex]
Simplify inside the parentheses:
[tex]\[ x + 8 = 2 \times 13 \][/tex]
[tex]\[ x + 8 = 26 \][/tex]
To solve for [tex]\( x \)[/tex], subtract 8 from both sides:
[tex]\[ x = 26 - 8 \][/tex]
[tex]\[ x = 18 \][/tex]
So from the second equation, [tex]\( x = 18 \)[/tex] when [tex]\( y = 5 \)[/tex].
Thus, the solution to the system of equations is:
- From the first equation: [tex]\( x = 24 \)[/tex]
- From the second equation: [tex]\( x = 18 \)[/tex]
And for both cases, [tex]\( y = 5 \)[/tex].
So the results are:
[tex]\[ (x, y) = (24, 5) \text{ in the first equation} \][/tex]
[tex]\[ (x, y) = (18, 5) \text{ in the second equation} \][/tex]
