Question

Solve the following system of equations by the elimination method:

11x – 16y = 35, 4x – 9y = 0

Answer 1

Given system of equations:

11x – 16y = 35   ...(i) 

4x – 9y = 0   ...(ii)

Step 1: Make the coefficients of one variable equal.

Multiply equation (ii) by 4 to align the coefficient of (x) with that in (i):

4 × (4x – 9y) = 4 × 0 

⇒ 16x – 36y = 0   ...(iii)

Multiply equation (i) by –4 to facilitate elimination: 

–4 × (11x – 16y) = –4 × 35 

⇒ –44x + 64y = –140   ...(iv)

Step 2: Add equations (iii) and (iv) to eliminate (x): 

(16x – 36y) + (–44x + 64y) = 0 + (–140) 

(16x – 44x) + (–36y + 64y) = –140 

–28x + 28y = –140

Step 3: Simplify: 

–28x + 28y = –140

⇒ –x + y = –5

⇒ y = x – 5

Step 4: Substitute (y = x – 5) into equation (ii): 

4x – 9y = 0 

4x – 9(x – 5) = 0 

4x – 9x + 45 = 0 

–5x + 45 = 0

⇒ –5x = –45

⇒ x = 9

Step 5: Find (y): 

y = x – 5

y = 9 – 5

y = 4

The solution to the system is x = 9, y = 4.