![]() Now, substituting the value of y in equation (ii), we get Worked-out problems on solving simultaneous linear equations: 1. Thus, x = 2 and y = 1 is the solution of the given system of equations. In 2ⁿᵈ equation, 2x + 3y = 7, put x = 2 and y = 1 in L.H.S. = x + y = 2 + 1 = 3, which is equal to R.H.S. Put x = 2 and y = 1 in the equation x + y = 3 (ii) Show that x = 2 and y = 1 is the solution of the system of linear equation x + y = 3and 2x + 3y = 7 If we take x = 7 and y = 5, then the two equations are satisfied, so we say (7, 5) is the solution of the given simultaneous linear equations. ![]() (i) x + y = 12 and x – y = 2 are two linear equation (simultaneous equations). Simultaneous equations formed from the problems: Therefore, second condition gives: 7x + 3y = 43 Step III: Express the conditions of the problem in terms of x and y Therefore, first condition gives: 3x – 2y = 2 Step II: Identify the relation between the unknown quantities. Here two unknown quantities (variables) are: Step I: Indentify the unknown variables assume one of them as x and the other as y Also, total price of 7 pencil cutters and 3 pens is $43.įollow the steps of instruction along with the method of solution. Let us take a mathematical problem to indicate the necessary steps for forming simultaneous equations: In a stationery shop, cost of 3 pencil cutters exceeds the price of 2 pens by $2. Necessary steps for forming and solving simultaneous linear equations The solution of system of simultaneous linear equation is the ordered pair (x, y) which satisfies both the linear equations. Two linear equations in two variables taken together are called simultaneous linear equations. (Both equations having to same variable i.e., x, y) Simultaneous linear equations: Here, we will learn about two linear equations in 2 variables. The graph of linear equation ax + by + c = 0 is always a straight line.Įvery linear equation in two variables has an infinite number of solutions. Where a, b, c are constant (real number) and at least one of a and b is non-zero. We have already learnt that linear equation in two variable x and y is in the form ax + by + c = 0.
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