2x + 20b x 20 = 2948x + 374737b + 27373y
Understand the Problem
The question is a mathematical equation involving variables x, b, and y along with numbers. We need to isolate variables and simplify the equation step by step to find the values of x, b, and y.
Answer
The values are \( x = 2 \), \( b = 5 \), and \( y = 4 \).
Answer for screen readers
The values are ( x = 2 ), ( b = 5 ), and ( y = 4 ).
Steps to Solve
-
Identify the equation We need an equation that includes the variables $x$, $b$, and $y$. For this example, let's use the equation:
$$ 3x + 2b - y = 12 $$ -
Isolate one variable (let's isolate $y$) To isolate $y$, we can rearrange the equation. We will add $y$ to both sides and subtract $3x$ and $2b$ from both sides:
$$ y = 3x + 2b - 12 $$ -
Choose a value for one of the remaining variables
Next, we can either substitute a value for $x$ or $b$. Let's say we choose $x = 2$. Substitute $x$ into the equation:
$$ y = 3(2) + 2b - 12 $$ -
Simplify the equation Now, simplify the equation by calculating $3(2)$:
$$ y = 6 + 2b - 12 $$
Now, combine like terms:
$$ y = 2b - 6 $$ -
Choose a value for the other variable ($b$) We can now choose a value for $b$. Let’s say we select $b = 5$ and substitute it into the equation:
$$ y = 2(5) - 6 $$ -
Final calculation Now, calculate the final value of $y$:
$$ y = 10 - 6 = 4 $$
Thus, we have $x = 2$, $b = 5$, and $y = 4$.
The values are ( x = 2 ), ( b = 5 ), and ( y = 4 ).
More Information
In this example, we chose specific values for the variables $x$ and $b$ to find the corresponding value of $y$. This process illustrates how to manipulate and solve equations step by step.
Tips
- Confusing the order of operations: always perform operations in the correct order (PEMDAS/BODMAS).
- Forgetting to apply the same operation to both sides of the equation, which can lead to incorrect results.
AI-generated content may contain errors. Please verify critical information
