Question

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

9x – 4y = 200, 7x – 3y = 200

Answer 1

Given system of simultaneous linear equations:

9x – 4y = 200

7x – 3y = 200

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

9x – 4y – 200 = 0

7x – 3y – 200 = 0

So, a₁ = 9, b₁ = –4, c₁ = –200 

a₂ = 7, b₂ = –3, c₂ = –200

Using the cross-multiplication method:

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

`x = ((-4)(-200) - (-3)(-200))/(9 xx (-3) -7 xx (-4))`

`x = (800 - 600)/(-27 + 28)`

`x = 200/1`

x = 200

`y = (a_2c_1 - a_1c_2)/(a_1b_2 - a_2b_1)`

`y = (7 xx (-200) - 9 xx (-200))/(9 xx (-3) - 7 xx (-4))`

`y = (-1400 + 1800)/(-27 + 28)`

`y = 400/1`

y = 400

Thus, the solution of the system by cross-multiplication is x = 200, y = 400.