Linear Equations in Two Variables

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A linear equation in two variables is an equation that contains two variables where the degree of each term containing a variable is one. The general form is ax + by + c = 0, where a, b, c are real nu…

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No, this is not a linear equation in two variables because the term 3x² has degree 2 (the variable x is squared), which violates the condition that each term containing a variable should have degree 1…

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When we consider two linear equations in two variables at the same time, they are called simultaneous linear equations. For example: x + y = 4 and 2x - y = 2 are simultaneous equations.

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The graph of a linear equation in two variables is always a straight line. Each ordered pair (x, y) that satisfies the equation represents a point on this line.

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Theoretically, only two points are needed to draw a straight line. However, we often plot 3-4 points to avoid errors. If coordinates of one point are wrong, plotting more points helps identify the mis…

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Step 1: Find ordered pairs for both equations For x + y = 4: (0,4), (4,0), (2,2) For 2x - y = 2: (0,-2), (1,0), (2,2) Step 2: Plot points and draw lines Step 3: Find intersection point Solution: x = 2…

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When two equations have the same graph, they represent the same line (coincident lines). This means the equations are equivalent and have infinitely many solutions. Every point on the line satisfies b…

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A determinant is a special number calculated from a square array of numbers. For a 2×2 determinant |a b|/|c d|, the value is ad - bc. Example: |2 3|/|1 4| = (2×4) - (3×1) = 8 - 3 = 5.