Simultaneous (Linear) Equations
ICSE · Class 9 · Mathematics
Flashcards for Simultaneous (Linear) Equations — ICSE Class 9 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Explore the full setSolve by inspection: 2x - y = 1 and 3x + y = 14. What values of x and y satisfy both equations?
Answer
Step 1: Try x = 3 and y = 5. Step 2: Check 2x - y = 2(3) - 5 = 6 - 5 = 1. Step 3: Check 3x + y = 3(3) + 5 = 9 + 5 = 14. Answer: x = 3, y = 5.
Solve using substitution: x + y = 7 and 3x - 2y = 11.
Answer
Step 1: From x + y = 7, write y = 7 - x. Step 2: Substitute in 3x - 2y = 11. 3x - 2(7 - x) = 11 3x - 14 + 2x = 11 5x = 25 x = 5 Step 3: Put x = 5 in y = 7 - x. y = 7 - 5 = 2 Answer: x = 5, y = 2.
Apply substitution to a pair with fractions: Solve 7/x + 8/y = 2 and 2/x + 13/y = 22.
Answer
Step 1: Let a = 1/x and b = 1/y. Then 7a + 8b = 2 and 2a + 13b = 22. Step 2: Multiply the first equation by 2 and the second by 7. 14a + 16b = 4 14a + 91b = 154 Step 3: Subtract. 75b = 150 b = 2, so 1…
When do you use the method of equating coefficients? Solve: 3x - 4y = 10 and 5x - 3y = 24.
Answer
Use this method when one variable can be made equal in both equations by multiplying with suitable numbers. Step 1: Multiply the first equation by 5 and the second by 3. 15x - 20y = 50 15x - 9y = 72 S…
Why do symmetric-coefficient equations like 65x - 33y = 97 and 33x - 65y = 1 get solved by adding and subtracting?
Answer
Because the coefficient of x in one equation matches the coefficient of y in the other, and the reverse is also true. That makes addition and subtraction remove one unknown quickly. Step 1: Add the eq…
Solve by cross-multiplication: 4x - 7y + 28 = 0 and 7x - 5y - 9 = 0.
Answer
Step 1: Write in standard form a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0. Here, a1 = 4, b1 = -7, c1 = 28; a2 = 7, b2 = -5, c2 = -9. Step 2: Use cross-multiplication. Denominator = a1b2 - a2b1 = 4(-5) …
Formula for x in cross-multiplication.
Answer
If a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, then x = (b1c2 - b2c1) / (a1b2 - a2b1). Meaning: b1, c1, a1 come from the first equation and b2, c2, a2 come from the second equation. Quick check: for 2x…
Formula for y in cross-multiplication.
Answer
If a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, then y = (c1a2 - c2a1) / (a1b2 - a2b1). Meaning: c1 and a1 come from the first equation, c2 and a2 from the second. Quick check: for 3x + y - 13 = 0 and x…
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