Question

write the linear equation represented by line ab and PQ. also find the coordinate of intersection of line AB and PQ ​

Answer 1

Two lines AB and PQ can be represented by the linear equations in two variables, A₁x+B₁y+C₁=0 and A₂x+B₂y+C₂=0, and the coordinates of their point of intersection are given by the solutions of these equations.

• A linear equation is an equation of degree one, i.e. an equation whose each variable is of power one.
• The standard form of linear equations in two variables is given by Ax + By = C, where A, B and C are constants, and x and y are the variables.
• The graph of a linear equation in two variables is a straight line.
• Two linear equations in two variables, A₁x+B₁y+C₁=0 and A₂x+B₂y+C₂=0, represent two lines that intersect only for values of the zeroes of both equations.
• Two linear equations in two variables form simultaneous linear equations.
• There are various ways of solving simultaneous linear equations in two variables such as the graphical method, the substitution method, the elimination method, the cross-multiplication method and the determinant method.

Therefore, two lines AB and PQ can be represented by the linear equations in two variables, A₁x+B₁y+C₁=0 and A₂x+B₂y+C₂=0, and the coordinates of their point of intersection are given by the solutions of their equations.

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