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**.

● **Simultaneous Linear Equations**

**Solvability of Linear Simultaneous Equations**

**Word Problems on Simultaneous Linear Equations**

**Word Problems on Simultaneous Linear Equations**

**Practice Test on Word Problems Involving Simultaneous Linear Equations**

● **Simultaneous Linear Equations - Worksheets**

**Worksheet on Simultaneous Linear Equations**

**Worksheet on Problems on Simultaneous Linear Equations**

**8th Grade Math Practice****From Comparison Method to HOME PAGE**

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