Sure, let's break down the problem step by step and find the value of [tex]\( y \)[/tex].
### Step 1: Translating the problem into equations
We are given two pieces of information:
1. Three times [tex]\( x \)[/tex] is 13 less than [tex]\( y \)[/tex].
2. The sum of [tex]\( x \)[/tex] and two times [tex]\( y \)[/tex] is 12.
Translating these statements into equations:
1. [tex]\( 3x = y - 13 \)[/tex]
2. [tex]\( x + 2y = 12 \)[/tex]
### Step 2: Solving the system of equations
We have two equations:
[tex]\[ 3x = y - 13 \quad (1) \][/tex]
[tex]\[ x + 2y = 12 \quad (2) \][/tex]
First, solve equation (1) for [tex]\( y \)[/tex]:
[tex]\[ y = 3x + 13 \quad (1') \][/tex]
### Step 3: Substituting into the second equation
Substitute equation (1') into equation (2):
[tex]\[ x + 2(3x + 13) = 12 \][/tex]
[tex]\[ x + 6x + 26 = 12 \][/tex]
[tex]\[ 7x + 26 = 12 \][/tex]
Subtract 26 from both sides:
[tex]\[ 7x = 12 - 26 \][/tex]
[tex]\[ 7x = -14 \][/tex]
Divide by 7:
[tex]\[ x = -2 \][/tex]
### Step 4: Finding the value of [tex]\( y \)[/tex]
Substitute [tex]\( x = -2 \)[/tex] back into equation (1'):
[tex]\[ y = 3(-2) + 13 \][/tex]
[tex]\[ y = -6 + 13 \][/tex]
[tex]\[ y = 7 \][/tex]
So, the value of [tex]\( y \)[/tex] is [tex]\(\boxed{7}\)[/tex].
