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Maths — LINEAR EQUATIONS IN TWO VARIABLES
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Frequently Asked Questions
A linear equation in two variables is an equation that can be written in the form ax+by+c=0, where a and b are real numbers, and a and b are not both zero.
Key topics include forming linear equations, representing them graphically, finding solutions, and understanding methods like substitution, elimination, and cross multiplication.
The standard form is ax + by + c = 0.
The coefficients ‘a’ and ‘b’ determine the slope and orientation of the straight line on the Cartesian plane.
It has infinitely many solutions, each corresponding to a point on its straight-line graph.
It is represented by a straight line on the Cartesian plane, showing all possible (x, y) solutions.
Examples include x+y=5, 2x-3y=7, and 4x+y=9.
Only if the constant term c=0; otherwise, (0, 0) may not satisfy the equation.
A one-variable equation has a single solution represented by a point on the number line, while a two-variable equation has infinite solutions represented by a line.
It refers to all pairs (x,y) that satisfy the equation and make both sides equal.
By choosing different values of x, calculating corresponding y values, plotting those points, and joining them to form a straight line.
It is y=mx+c, where m is the slope of the line andcccis the y-intercept.
It shifts the line horizontally or vertically depending on its value.
They are solved by methods like substitution, elimination, graphical interpretation, or cross multiplication.
Because real-life problems often require solving two related conditions simultaneously, such as profit and cost or speed and time.