LINEAR EQUATIONS IN TWO VARIABLES
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.
They are two or more equations that have the same variables and are solved together to find a common solution.
Two lines have a unique solution if they intersect at exactly one point.
When their graphs are parallel lines that never meet.
When both lines coincide or represent the same line.
The horizontal axis (x-axis) and vertical axis (y-axis), used to locate points in the Cartesian plane.
An ordered pair is a set (x,y) that shows the specific position of a point in the Cartesian plane.
Graphs visually demonstrate the relationship between two variables and the nature of their solutions.
By translating word problems involving proportional or relational quantities into equations using variables for unknowns.
Examples include cost and quantity, time and distance, or simple profit and loss relationships.
This chapter forms the foundation for algebra, coordinate geometry, and future concepts like linear programming and simultaneous equations.
