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 setWhat is a linear equation in two variables? Give the general form.
Answer
A linear equation in two variables is an equation of the form ax + by + c = 0, where: - a, b, and c are constants (real numbers) - x and y are variables - Each variable has degree 1 (power 1) Example:…
What are simultaneous linear equations? Give an example.
Answer
Simultaneous linear equations are two or more linear equations that contain the same variables and are solved together to find common values of the variables. Example: 2x + 3y = 7 4x - y = 1 These e…
What is the solution of simultaneous equations 2x - y = 1 and 3x + y = 14?
Answer
To verify: x = 3, y = 5 Checking in first equation: 2(3) - 5 = 6 - 5 = 1 ✓ Checking in second equation: 3(3) + 5 = 9 + 5 = 14 ✓ Therefore, x = 3 and y = 5 is the solution as it satisfies both equat…
List the three algebraic methods for solving simultaneous equations.
Answer
The three algebraic methods are: 1. Method of elimination by substitution 2. Method of elimination by equating coefficients 3. Method of cross-multiplication Each method is useful in different situa…
Describe the steps for solving simultaneous equations by substitution method.
Answer
Steps for substitution method: Step 1: From either equation, express one variable in terms of the other Step 2: Substitute this expression in the other equation and solve for one variable Step 3: Sub…
Solve using substitution method: x + y = 7 3x - 2y = 11
Answer
Solution: Step 1: From x + y = 7, we get y = 7 - x Step 2: Substitute in second equation: 3x - 2(7 - x) = 11 3x - 14 + 2x = 11 5x = 25 x = 5 Step 3: y = 7 - x = 7 - 5 = 2 Answer: x = 5, y = 2…
Describe the steps for solving simultaneous equations by elimination (equating coefficients) method.
Answer
Steps for elimination method: Step 1: Multiply one or both equations by suitable numbers to make coefficients of one variable numerically equal Step 2: Add or subtract the equations to eliminate one …
Solve using elimination method: 3x - 4y = 10 5x - 3y = 24
Answer
Solution: Step 1: Multiply first equation by 5 and second by 3: 15x - 20y = 50 15x - 9y = 72 Step 2: Subtract first from second: -9y - (-20y) = 72 - 50 11y = 22 y = 2 Step 3: Substitute y = 2 in fir…
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