To solve the system of equations:

\[
\begin{align*}
1) & \quad 2x + 3y = 7 \\
2) & \quad x = 1 - 4y
\end{align*}
\]

We can use substitution or elimination. Let's use substitution since \( x \) is already expressed in terms of \( y \) in the second equation.

### Step 1: Substitute the value of \( x \) from equation 2 into equation 1.
\[
2(1 - 4y) + 3y = 7
\]

### Step 2: Expand and simplify.
\[
2 - 8y + 3y = 7
\]
\[
2 - 5y = 7
\]

### Step 3: Solve for \( y \).
\[
-5y = 7 - 2
\]
\[
-5y = 5
\]
\[
y = -1
\]

### Step 4: Substitute \( y = -1 \) back into the expression for \( x \) from equation 2.
\[
x = 1 - 4(-1)
\]
\[
x = 1 + 4
\]
\[
x = 5
\]

### Final Solution:
The solution to the system of equations is:
\[
x = 5, \quad y = -1
\]

Would you like more details on any step or have any questions?

### Related Questions:
1. How do you solve a system of linear equations using the elimination method?
2. What are the conditions for a system of linear equations to have a unique solution?
3. How can you graphically interpret the solution to this system of equations?
4. What happens if you change the coefficients in the equations slightly?
5. How do you solve a system of three linear equations with three variables?

### Tip:
Always check your solution by substituting the values back into the original equations to ensure they satisfy both equations.

Learn how to solve the system of linear equations 2x + 3y = 7 and x = 1 - 4y using the substitution method with a detailed step-by-step solution. This problem covers systems of linear equations and substitution method concepts. Suitable for students in Grades 8-10.

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