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Linear Equations in Two Variables Video Lecture | Quantitative Aptitude (Quant) - CAT
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FAQs on Linear Equations in Two Variables Video Lecture - Quantitative Aptitude (Quant) - CAT
| 1. What are linear equations in two variables? |  |
Ans. Linear equations in two variables are mathematical expressions that represent a straight line when graphed on a coordinate plane. They are typically written in the form of \( ax + by = c \), where \( a \), \( b \), and \( c \) are constants, and \( x \) and \( y \) are the variables.
| 2. How do you solve linear equations in two variables? | |
Ans. To solve linear equations in two variables, you can use methods such as graphing, substitution, or elimination. Graphing involves plotting the equations on a coordinate plane and finding the point where they intersect. Substitution involves solving one equation for one variable and substituting that value into the other equation. Elimination involves adding or subtracting the equations to eliminate one variable.
| 3. What is the graphical representation of a linear equation in two variables? | |
Ans. The graphical representation of a linear equation in two variables is a straight line. Each point on the line represents a solution to the equation. The slope of the line indicates the rate of change between the variables, while the y-intercept shows where the line crosses the y-axis.
| 4. Can a linear equation in two variables have more than one solution? | |
Ans. Yes, a linear equation in two variables can have infinitely many solutions, as every point on the line is a solution. However, if you have a system of two linear equations, they can either intersect at one point (one solution), be parallel and never intersect (no solution), or coincide (infinitely many solutions).
| 5. What is the significance of the coefficients in a linear equation in two variables? | |
Ans. The coefficients in a linear equation in two variables indicate the relationship between the two variables. The coefficient of \( x \) represents how much \( y \) changes for a unit change in \( x \) (slope), while the coefficient of \( y \) shows how much \( x \) changes for a unit change in \( y \). Together, they define the angle and direction of the line in the coordinate plane.
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