What is Checking a Solution by Substituting Back?

S1-SA5-1189

Grade Level:

Class 5

Maths, Computing, AI, Physics, Science

Definition

What is it?

Checking a solution by substituting back means putting your answer for a variable back into the original problem's equation or statement to see if it makes sense and is correct. It's like re-running a calculation with your found answer to verify it works perfectly.

Simple Example

Quick Example

Imagine you solved a puzzle: 'I have some laddoos. If I give 3 away, I will have 5 left. How many laddoos did I start with?' You found the answer to be 8 laddoos. To check, you 'substitute back': if you start with 8 laddoos and give 3 away, 8 - 3 = 5. Since 5 is what was expected, your answer 8 is correct!

Worked Example

Step-by-Step

PROBLEM: Reema bought a new tiffin box for Rs 120 and a water bottle. The total cost was Rs 250. How much did the water bottle cost?

Step 1: Understand the problem. Let 'x' be the cost of the water bottle.
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Step 2: Write the equation: Cost of tiffin box + Cost of water bottle = Total cost. So, 120 + x = 250.
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Step 3: Solve for x. Subtract 120 from both sides: x = 250 - 120.
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Step 4: Calculate x. x = 130. So, the water bottle cost Rs 130.
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Step 5: Now, check your answer by substituting back into the original equation: 120 + x = 250.
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Step 6: Replace 'x' with your answer, 130: 120 + 130 = 250.
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Step 7: Calculate the left side: 120 + 130 = 250.
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Step 8: Compare both sides: 250 = 250. Since both sides are equal, your answer x = 130 is correct!

Why It Matters

This skill is super important in Maths, Computing, and Science because it helps you confirm your calculations and code are accurate. Engineers use it to double-check their designs, and even AI programmers use it to verify their models' predictions. It ensures your solutions are reliable, just like a scientist verifying an experiment.

Common Mistakes

MISTAKE: Not substituting into the ORIGINAL equation, but into a modified one. | CORRECTION: Always use the very first equation or problem statement you wrote down to check your answer.

MISTAKE: Making a calculation error while substituting back, leading you to think your correct answer is wrong. | CORRECTION: Be extra careful and double-check your arithmetic when substituting back.

MISTAKE: Only checking one part of a multi-step problem. | CORRECTION: Ensure you substitute your final answer back into the overall problem to see if it satisfies all conditions.

Practice Questions

Try It Yourself

QUESTION: If a number 'y' plus 7 equals 15 (y + 7 = 15), and you found y = 8. Check if your answer is correct by substituting back. | ANSWER: 8 + 7 = 15. Since 15 = 15, the answer is correct.

QUESTION: My friend has 'x' cricket cards. If he buys 12 more, he will have 30 cards. You calculated x = 18. Check this answer. | ANSWER: 18 + 12 = 30. Since 30 = 30, the answer is correct.

QUESTION: A taxi charges Rs 50 as a base fare plus Rs 10 per kilometer. If your total bill was Rs 150 for a trip, you found the distance was 10 km. Use the formula (Total Bill = Base Fare + (Rate per km * Distance)) to check your answer. | ANSWER: Total Bill = 50 + (10 * 10) = 50 + 100 = 150. Since 150 = 150, the answer is correct.

MCQ

Quick Quiz

Why is substituting back a good practice?

It makes the problem harder to solve.

It helps you confirm your answer is correct.

It is only useful for very difficult problems.

It changes the original problem.

The Correct Answer Is:

Substituting back helps you verify if the answer you found actually works in the original problem, confirming its correctness. It doesn't make the problem harder or change it, nor is it only for difficult problems.

Real World Connection

In the Real World

When you buy groceries and the shopkeeper gives you a bill, you mentally (or with a calculator) check if the total amount matches the sum of all individual item prices. This is a form of substituting back! Similarly, a software developer checks if a new feature works correctly by testing it with expected inputs and seeing if the output matches, just like substituting your answer back into the problem.

Key Vocabulary

Key Terms

SUBSTITUTE: To replace a variable (like 'x') with a specific value or number. | EQUATION: A mathematical statement showing that two expressions are equal (e.g., 2 + x = 5). | VARIABLE: A letter or symbol that represents an unknown number or value. | VERIFY: To confirm that something is true or accurate. | SOLUTION: The answer to a problem or equation.

What's Next

What to Learn Next

Great job learning to check your answers! Next, explore 'Solving Equations with One Variable' to build on this. Knowing how to check your work will make you super confident as you tackle more complex math problems!