Key Points
Key Points: Substitution Method
Steps:
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Express one variable in terms of the other
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Substitute
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Solve
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Substitute back
| Case | What You Get While Solving | Type of Statement | Nature of Equations |
|---|---|---|---|
| Unique solution | Specific values of x and y | Valid numerical values | Consistent |
| Infinitely many solutions | A true statement like 18 = 18 | Always true | Dependent |
| No solution | A false statement like 0 = 5 | Contradiction | Inconsistent |
Key Points: Elimination Method
Steps:
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Multiply one or both equations
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Add or subtract
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Solve
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Substitute
| Case | Result While Solving | Type of Statement | Nature of Pair |
|---|---|---|---|
| Unique solution | You get a specific value of x (or y) | Valid numerical value | Consistent |
| Infinitely many solutions | You get a true statement (e.g. 18 = 18) | Always true | Dependent |
| No solution | You get a false statement (e.g. 0 = 9) | Contradiction | Inconsistent |
Important Questions [6]
- Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method: If we add 1 to the numerator and subtract 1 from the denominator,
- A fraction becomes 1 2 when 2 is subtracted from the numerator and it becomes 1 2 when 1 is subtracted from the denominator. Find the fraction.
- A fraction becomes 1/3 when 2 is subtracted from the numerator and it becomes 1/2 when 1 is subtracted from the denominator. Find the fraction.
- A 2-digit number is such that the product of its digits is 24. If 18 is subtracted from the number, the digits interchange their places. Find the number.
- Read the following passage: Two schools 'P' and 'Q' decided to award prizes to their students for two games of Hockey ₹ x per student and Cricket ₹ y per student.
- Rehana went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹ 50 and ₹ 100 notes only. Rehana got 25 notes in all. Find how many notes of ₹ 50 and ₹ 100 did she received.
