Problem Description:
The task involves solving a linear equation step by step. The given equation is:
\[
2x + 4y = 6x + 3y
\]
The steps provided in the image are as follows:
1. Subtract \(6x\) from both sides.
2. Combine \(2x\) and \(-6x\) to get \(-4x\).
3. Subtract \(4y\) from both sides.
4. Combine \(3y\) and \(-4y\) to get \(-y\).
We need to verify these steps and solve the equation completely.
---
Step-by-Step Solution:
####
Step 1: Start with the given equation
\[
2x + 4y = 6x + 3y
\]
####
Step 2: Subtract \(6x\) from both sides
Subtracting \(6x\) from both sides helps isolate the \(x\)-terms on one side:
\[
2x + 4y - 6x = 6x + 3y - 6x
\]
Simplify:
\[
(2x - 6x) + 4y = 3y
\]
\[
-4x + 4y = 3y
\]
####
Step 3: Subtract \(4y\) from both sides
Subtracting \(4y\) from both sides helps isolate the \(y\)-terms on one side:
\[
-4x + 4y - 4y = 3y - 4y
\]
Simplify:
\[
-4x = -y
\]
####
Step 4: Solve for \(y\) in terms of \(x\)
To express \(y\) in terms of \(x\), divide both sides by \(-1\):
\[
y = 4x
\]
---
Final Answer:
The solution to the equation is:
\[
\boxed{y = 4x}
\]
---
Explanation of the Solution:
1.
Subtracting \(6x\): This step isolates the \(x\)-terms on one side of the equation, making it easier to combine like terms.
2.
Combining like terms: After subtracting \(6x\), we combine \(2x\) and \(-6x\) to get \(-4x\). Similarly, after subtracting \(4y\), we combine \(3y\) and \(-4y\) to get \(-y\).
3.
Isolating \(y\): Finally, dividing both sides by \(-1\) gives the relationship \(y = 4x\).
This process ensures that the equation is solved correctly and systematically.
Parent Tip: Review the logic above to help your child master the concept of algebra solver.
