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What are Linear Equations in One Variable? Video Lecture | Mathematics for EmSAT Achieve
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| 1. What is a linear equation in one variable? |  |
Ans. A linear equation in one variable is an algebraic equation that can be written in the form ax + b = 0, where "x" represents the variable, "a" and "b" are constants, and "a" is not equal to zero. It represents a straight line when plotted on a graph.
| 2. How do you solve a linear equation in one variable? | |
Ans. To solve a linear equation in one variable, isolate the variable on one side of the equation by performing operations such as addition, subtraction, multiplication, and division on both sides. The goal is to simplify the equation until you obtain the value of the variable.
| 3. Can a linear equation have more than one solution? | |
Ans. Yes, a linear equation can have more than one solution. This occurs when the equation is true for multiple values of the variable. For example, the equation 2x + 4 = 8 has the solution x = 2, but it is also true for x = 3, x = 4, and so on.
| 4. What does the slope of a linear equation represent? | |
Ans. The slope of a linear equation represents the rate of change or the steepness of the line. It indicates how much the dependent variable (y) changes for each unit increase in the independent variable (x). A positive slope means the line rises from left to right, while a negative slope means it falls.
| 5. Can a linear equation have no solution? | |
Ans. Yes, a linear equation can have no solution. This occurs when the equation is contradictory and cannot be satisfied by any value of the variable. For example, the equation 2x + 4 = 2x + 6 has no solution because no value of x can make the equation true.
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