Q1. Solve the system of equations by the addition method:

Background

Topic: Systems of Linear Equations (Addition/Elimination Method)

This question tests your ability to solve a system of two linear equations using the addition (also called elimination) method. The goal is to combine the equations in such a way that one variable is eliminated, allowing you to solve for the other.

Key Terms and Formulas

• System of equations: Two or more equations with the same variables.

• Addition/Elimination method: A technique where you add or subtract equations to eliminate one variable.

• Linear equation: An equation of the form .

Step-by-Step Guidance

1. Write both equations clearly:

2. Decide which variable to eliminate. Let's try to eliminate by making the coefficients of $y$ opposites. To do this, multiply the first equation by $4 so the $y$ terms become and :

   • First equation:

   • Second equation:

3. Multiply out both equations:

4. Add the two new equations together to eliminate :

Try solving on your own before revealing the answer!