Solve the following system of equations by the Method of Comparison Substituting this value of one of the variables in any one of the earlier equations, find out the value of the other variable.Equate these two values to obtain an equation in one variable and solve for that variable. These two values so obtained are obviously equal because and for all values of and.From the second equation also, we express the value of in terms of. From the first equation we express the value of in terms of. For example, say we have a pair of simultaneous equations in and. From the second equation find the value of the same unknown quantity in terms of the other.From the first equation find the value of any one unknown quantity in terms of the other.The third method of solving simultaneous equations viz., Method of Comparison will be covered in the articleВ Simultaneous Equations II. Note: It should be kept in mind that whatever method is undertaken for solving the pair of simultaneous equations the solution will remain the same, i.e., it is immaterial which method one chooses to solve a given pair of simultaneous equations. Step 4: Substituting this value of in equation (1) we have, Step 2: Adding equations (3) and (1) we have, Hence, it can be safely concluded that, which variable we choose to eliminate will not alter the solution in any way. Subtracting equation (4) from equation (3) we have, We multiply equation (1) by 3 and equation (2) by 4. Then we would have eliminated and arrive at an equation only in. We could have chosen the numbers in such a manner that the coefficients of would have become equal. Note: Here we have chosen the numbers to be multiplied such that the coefficients of become equal and we can thus eliminate and arrive at an equation only in as can be seen in steps 2 and 3. Step 4: Substituting in equation (1) we get, Step 2: Subtracting equation (4) from equation (3) we have, Step 1: We multiply equation (1) by 5 and equation (2) by 3. Solve the following system of equations by the Method of Elimination Substitute this value in any of the two equations given and find the value of the other unknown.Solve the resulting equation to find the value of the one of the unknowns.Add or subtract one equation from the other so that the terms with equal numerical coefficients cancel mutually and what remains is an equation containing either only or only.Multiply one or both of the equations by a suitable number or numbers so that either the coefficients of or the coefficients of in both the equations become numerically equal.Step 2: Substituting this value in the first equation we have, Step 1: From the second equation we have, Solve the following system of equations by the Method of Substitution Substituting the value of the variable obtained in step 2 above, in the result of step 1, get the value of the remaining unknown variable.Substitute the value of the variable, obtained in step 1 above, in the other equation and solve it to get the value of one variable.From any of the given two equations find the value of one variable in terms of other.The methods for solving simultaneous equations are as follows: Methods of Solving Simultaneous Equations

To solve two simultaneous linear equations means to find the values of unknown variables and satisfying both the given conditions. These equations are linear simultaneous equations or simple simultaneous equations because the maximum power of the variables involved in them is 1. Each of these two equations contains two variables (namely and ) and together these equations are called simultaneous (linear) equations. Two or more equations which are all satisfied by a single set of values of the involved variables are called simultaneous equations.Д¬onsider the two linear equations and. These equations may be individually satisfied for all values of the unknown quantities, but there is only one set of values of which will satisfy all three equations simultaneously. These equations will be satisfied by the same values of only when. Thus, the two equations will both be satisfied by the same pair of values of and only when andДЄgain, let us consider the following equations: However, if, together with this equation we consider the equation then and must be such that their difference is 2 and their sum is 8. We can safely say that this equation has an infinite number of solutions because any pair of numbers whose difference is 2 will satisfy the equation. It is very clear that this equation will hold true, i.e., be satisfied for all values of and. Let us consider the equation in which and are both unknown.

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