x = 2y -3                                                                                                                                                                                        3x + y = 7                              

To solve the system of linear equations:

\[
x = 2y - 3
\]
\[
3x + y = 7
\]

### Step 1: Substitute \( x = 2y - 3 \) into the second equation
Substituting the expression for \( x \) into the second equation gives:

\[
3(2y - 3) + y = 7
\]

### Step 2: Simplify and solve for \( y \)
Expand and simplify the equation:

\[
6y - 9 + y = 7
\]
\[
7y - 9 = 7
\]

Add 9 to both sides:

\[
7y = 16
\]

Divide both sides by 7:

\[
y = \frac{16}{7}
\]

### Step 3: Substitute \( y = \frac{16}{7} \) back into the first equation
Now, substitute the value of \( y \) back into the first equation to find \( x \):

\[
x = 2\left(\frac{16}{7}\right) - 3
\]
\[
x = \frac{32}{7} - 3
\]

Express 3 as a fraction with a denominator of 7:

\[
x = \frac{32}{7} - \frac{21}{7} = \frac{11}{7}
\]

### Final Answer:
The solution to the system of equations is:

\[
x = \frac{11}{7}, \quad y = \frac{16}{7}
\]

Would you like more details on any of the steps, or do you have any questions?

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Here are five related questions to explore further:

1. How do you solve a system of linear equations using the substitution method?
2. What is the graphical interpretation of solving two linear equations?
3. How would the solution change if the equations were parallel?
4. Can you solve a similar system of equations using the elimination method?
5. What happens if the system of equations has no solution or infinitely many solutions?

**Tip:** When dealing with fractions, keep your calculations in fractional form until the final step to maintain accuracy.

Learn how to solve a system of linear equations x = 2y - 3 and 3x + y = 7 using the substitution method with a detailed step-by-step solution. This problem covers key algebraic concepts, including linear equations and the substitution method. Suitable for students in Grades 7-9.

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