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Answer:
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 = 30
The 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 is
5x + 3(0) = 30
⇒ x = 6
and the value of y when x = 0 is,
5 (0) + 3y = 30
⇒ y = 10
Linear 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 = 12
Substituting the value of y in any of the equation (i) or (ii), we have
2x + 5(12) = 20
⇒ x = −20
Therefore, x=-20 and y =12 is the point where the given equations intersect.