Linear Equations in Two Variables — Flashcards
Maharashtra Board · Class 10 · Mathematics
25 flashcards for Linear Equations in Two Variables (Maharashtra Board Class 10 Mathematics) to test yourself on key terms and facts.
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Solve for y: 2x - y = 4 when x = 3.
Answer
Step 1: Substitute x = 3 into 2x - y = 4. 2(3) - y = 4 Step 2: Simplify. 6 - y = 4 Step 3: Subtract 6 from both sides. -y = -2 Step 4: Multiply by -1. y = 2 Answer: y = 2…
Solve the simultaneous equations: x + y = 4 and 2x - y = 2.
Answer
Step 1: Add the equations. (x + y) + (2x - y) = 4 + 2 3x = 6 Step 2: Solve for x. x = 2 Step 3: Substitute x = 2 in x + y = 4. 2 + y = 4 Step 4: Solve for y. y = 2 Answer: x = 2, y = 2…
Find two ordered pairs for the equation x + y = 4.
Answer
Step 1: Choose easy values of x. If x = 0, then y = 4, so one point is (0, 4). Step 2: Choose another value. If x = 2, then y = 2, so another point is (2, 2). Step 3: Check. 0 + 4 = 4 and 2 + 2 = 4. A…
Find the point of intersection of the lines x + y = 4 and 2x - y = 2.
Answer
Step 1: Solve the equations together. x + y = 4 2x - y = 2 Step 2: Add them. 3x = 6 x = 2 Step 3: Substitute x = 2 into x + y = 4. 2 + y = 4 y = 2 Step 4: The intersection point is the solution. Answe…
When do you use the graphical method for two linear equations in two variables?
Answer
Use it when you want to find the common point of two straight lines. Step 1: Draw each line using at least two ordered pairs. Step 2: See where the lines meet. Step 3: The meeting point gives the solu…
Why does a linear equation in two variables graph as a straight line?
Answer
Each equation gives many ordered pairs that satisfy it. Step 1: Plot a few satisfying points. Step 2: All points lie on one straight path. Step 3: That path is the graph of the equation. Example: For …
Write the general form of a linear equation in two variables and solve: 3x = 4y - 12 is written in what form?
Answer
General form: ax + by + c = 0 Step 1: Bring all terms to one side. 3x = 4y - 12 3x - 4y + 12 = 0 Step 2: Check the form. It matches ax + by + c = 0. Answer: 3x - 4y + 12 = 0…
Is 4m + 3n = 12 a linear equation in two variables?
Answer
Step 1: Check the powers of the variables. m and n each have degree 1. Step 2: Check the form. It can be written as 4m + 3n - 12 = 0. Step 3: Both variables are present and no variable is squared or i…
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