mark as brainlistAnswer:Linear Equations In Two Variables Definition:An equation that can be put in the form ax + by + c = 0, where a, b and c are real NUMBERS and a, b not EQUAL to ZERO is called a linear equation in two variables namely x and y. The solution for such an equation is a pair of values, one for x and one for y which further makes the two sides of an equation equal.Linear Equations In Two Variables Example:In order to find the solution of Linear equation in 2 variables,Consider for Example:5x + 3y = 30The above equation has two variables namely x and y.Graphically this equation can be represented by substituting the variables to zero.The value of x when y=0 is5x + 3(0) = 30⇒ x = 6and the value of y when x = 0 is,5 (0) + 3y = 30⇒ y = 10Linear Equations in Two Variables Questions:Question: Find the value of variables which satisfies the FOLLOWING equation:2x + 5Y = 20 and 3x+6y =12.Solution:Using the method of substitution to solve the pair of linear equation, we have:2x + 5y = 20…………………….(i)3x+6y =12……………………..(ii)Multiplying equation (i) by 3 and (ii) by 2, we have:6x + 15y = 60…………………….(iii)6x+12y = 24……………………..(iv)Subtracting equation (iv) from (iii)3y = 36⇒ y = 12Substituting the value of y in any of the equation (i) or (ii), we have2x + 5(12) = 20⇒ x = −20Therefore, x=-20 and y =12 is the point where the given equations intersect.