Question

Solve the following system of equations by the elimination method:

2bx + ay = 2ab, bx – ay = 4ab

Answer 1

Given system of equations:

2bx + ay = 2ab   ...(i) 

bx – ay = 4ab   ...(ii)

Step 1: Eliminate one variable

Multiply equation (ii) by 2 to align the coefficients of (bx) with equation (i): 

2(bx) – 2(ay) = 2(4ab) 

2bx – 2ay = 8ab   ...(iii)

Step 2: Subtract equation (i) from equation (iii) to eliminate (2bx): 

(2bx – 2ay) – (2bx + ay) = 8ab – 2ab 

2bx – 2ay – 2bx – ay = 6ab 

–3ay = 6ab

Step 3: Solve for (y): 

–3ay = 6ab

⇒ `y = (6ab)/(-3a)`

⇒ y = –2b

Step 4: Substitute (y = –2b) into equation (ii) to find (x):

bx – a(–2b) = 4ab 

bx + 2ab = 4ab 

bx = 4ab – 2ab

bx = 2ab

`x = (2ab)/(b)`

x = 2a