# Comparison Method

Steps to solve the system of linear equations by using the comparison method to find the value of x and y.

3x – 2y = 2 ---------- (i)

7x + 3y = 43 --------- (ii)

Now for solving the above simultaneous linear equations by using the method of comparison follow the instructions and the method of solution.

Step I: From equation 3x – 2y = 2 --------- (i), express x in terms of y.

Likewise, from equation 7x + 3y = 43 -------- (ii), express x in terms of y

From equation (i) 3x – 2y = 2 we get;

3x – 2y + 2y = 2 + 2y (adding both sides by 2y)

or, 3x = 2 + 2y

or, 3x/3 = (2 + 2y)/3 (dividing both sides by 3)

or, x = (2 + 2y)/3

Therefore, x = (2y + 2)/3 ---------- (iii)

From equation (ii) 7x + 3y = 43 we get;

7x + 3y – 3y = 43 – 3y (subtracting both sides by 3y)

or, 7x = 43 – 3y

or, 7x/7 = (43 – 3y)/7 (dividing both sides by 7)

or, x = (43 – 3y)/7

Therefore, x = (–3y + 43)/7 ---------- (iv)

Step II: Equate the values of x in equation (iii) and equation (iv) forming the equation in y

From equation (iii) and (iv), we get;

(2y + 2)/3 = (–3y + 43)/7 ---------- (v)

Step III: Solve the linear equation (v) in y

(2y + 2)/3 = (–3y + 43)/7 ---------- (v) Simplifying we get;

or, 7(2y + 2) = 3(–3y + 43)

or, 14y + 14 = –9y + 129

or, 14y + 14 – 14 = –9y + 129 – 14

or, 14y = -9y + 115

or, 14y + 9y = –9y + 9y + 115

or, 23y = 115

or, 23y/23 = 115/23

Therefore, y = 5

Step IV: Putting the value of y in equation (iii) or equation (iv), find the value of x

Putting the value of y = 5 in equation (iii) we get;

x = (2 × 5 + 2)/3

or, x = (10 + 2)/3

or, x = 12/3

Therefore, x = 4

Step V: Required solution of the two equations

Therefore, x = 4 and y = 5

Therefore, we have compared the values of x obtained from equation (i) and (ii) and formed an equation in y, so this method of solving simultaneous equations is known as the comparison method. Similarly, comparing the two values of y, we can form an equation in x.

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