Question

Using cross-multiplication method, solve the following system of simultaneous linear equations:

3x + 2y = 7, 2x + 3y = 8

Answer 1

Given system of linear equations:

3x + 2y = 7

2x + 3y = 8

Rewrite in the form (a₁x + b₁y + c₁ = 0) and (a₂x + b₂y + c₂ = 0):

3x + 2y – 7 = 0

⇒ a₁ = 3, b₁ = 2, c₁ = –7

2x + 3y – 8 = 0

⇒ a₂ = 2, b₂ = 3, c₂ = –8

Step 1: Calculate the determinants needed for cross-multiplication:

`x = (b_1c_2 - b_2c_1)/(a_1b_2 - a_2b_1)`

`x = (2 xx (-8) -3 xx (-7))/(3 xx 3 - 2 xx 2)`

`x = (-16 + 21)/(9 - 4)`

`x = 5/5`

x = 1

`y = (c_1a_2 - c_2a_1)/(a_1b_2 - a_2b_1)`

`y = (-7 xx 2 - (-8) xx 3)/(3 xx 3 - 2 xx 2)`

`y = (-14 + 24)/(9 - 4)`

`y = 10/5`

y = 2

The solution to the system is x = 1, y = 2.