Example 2: Write the given linear equation in its standard form, y = 5x. Solution: In order to rewrite the given equation in standard form, we will transpose the term 'y' to the right-hand side and we will write the constant as 0 on the left-hand side. This means it will become 0 = 5x - y. Then, we can flip the equation and write it as, 5x - y = 0.

Simultaneous linear equations in two variables involve two unknown quantities to represent real-life problems. It helps in establishing a relationship between quantities, prices, speed, time, distance, etc results in a better understanding of the problems. We all use simultaneous linear equations in our daily life without knowing it.

The linear equations in two variables are the equations in which each of the two variables is of the highest order of 1 and may have one, none, or infinitely many solutions.The standard form of a two-variable linear equation is ax + by + c = 0 where x and y are the two variables. The solutions can also be written in ordered pairs like (x, y). The graphical representation of the pairs of linear ...

Let us convert the standard form of a quadratic equation ax 2 + bx + c = 0 into the vertex form a (x - h) 2 + k = 0 (where (h, k) is the vertex of the quadratic function f(x) = a (x - h) 2 + k). Note that the value of 'a' is the same in both equations. Let us just set them equal to know the relation between the variables.