Year 10: Simultaneous linear equations word problems

This cheat sheet provides a quick guide to solving word problems involving simultaneous linear equations.

Key Steps

• Read Carefully: Understand the context of the problem and identify the variables.
• Formulate Equations: Translate the problem into two linear equations. Often, you'll need to use information given in the problem to create these equations. Look for key words like "total," "sum," "difference," "twice," "half," etc.
• Solve the Equations: Use methods like substitution or elimination to solve the two equations for the values of the variables.
• Check Your Answer: Substitute the values you found back into the original word problem to ensure they make sense and the problem is correctly solved.

Example

Problem: "The cost of a movie ticket and popcorn is $20. A movie ticket costs $12. What is the cost of the popcorn?"

Equations: Let x = cost of ticket, y = cost of popcorn.

x + y = 20

x = 12

Substitute x = 12 into the first equation: 12 + y = 20. Solve for y: y = 8

Therefore, the cost of popcorn is $8.