An appropriate first step to solve the system of equations below using the substitution method would be to multiply the top equation by 3. (Hint: not the addition method!!)
2x+y = 1
(-1/2)x-3y = -14

TRUE OR FALSE

The statement is **false**.

When using the **substitution method** to solve a system of equations, the goal is to solve one of the equations for one variable and then substitute that expression into the other equation. Multiplying the top equation by 3 would be a step typically associated with the **elimination method** (also known as the addition method), not the substitution method.

Here’s the correct approach for substitution:

1. Solve the first equation \( 2x + y = 1 \) for \( y \):
   \[
   y = 1 - 2x
   \]
   
2. Substitute \( y = 1 - 2x \) into the second equation:
   \[
   -\frac{1}{2}x - 3(1 - 2x) = -14
   \]

This process allows you to solve for \( x \) first, and then you can use the value of \( x \) to find \( y \).

Would you like further details on solving this system, or do you have any questions?

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**Relative Questions:**

1. How do you solve a system of equations using the substitution method?
2. What is the elimination method, and how does it differ from substitution?
3. Can you solve the system using substitution and verify the solution?
4. Why might multiplying an equation be helpful in solving systems by elimination?
5. How would the process change if both equations were already solved for \( y \)?
6. Can systems of equations have no solution or infinitely many solutions? How can we identify this?
7. What are the advantages and disadvantages of the substitution method compared to elimination?
8. What are the key indicators that suggest using substitution might be the best method?

**Tip:** When using the substitution method, always choose the equation and variable that makes the substitution simplest to avoid complicated algebraic expressions.

Explore how to solve systems of equations using the substitution method with a detailed explanation. This problem involves understanding the difference between substitution and elimination methods in solving linear equations. Suitable for high school students.

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