Question

Solve, using cross-multiplication :
0.4x - 1.5y = 6.5
0.3x + 0.2y = 0.9

Answer 1

Given equation are 0.4x - 1.5y = 6.5 and 0.3x + 0.2y = 0.9
Comparing with a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, We have

a₁ = 0.4, b₁ = -1.5, c₁ = -6.5 and a₂ = 0.3, b₂ = 0.2, c₂ = 0.9

Now, x = `[ b_1c_2 - b_2c_1 ]/[ a_1b_2 - a_2b_1 ]  and  y = [ c_1a_2 - c_2a_1 ]/[ a_1b_2 - a_2b_1 ]` 

⇒ x = `[( - 1.5) xx (-0.9) - ( 0.2 ) xx ( -6.5 )]/[ 0.4 xx (0.2) - (0.3) xx (-1.5) ]  and  y = [ (-6.5) xx (0.3) - (-0.9) xx (0.4) ]/[ 0.4 xx ( 0.2) - (0.3) xx (-1.5) ]`

⇒ x = `[ 1.35 + 1.3 ]/[ 0.08 + 0.45 ]  and y = [ -1.95 + 0.36 ]/[ 0.08 + 0.45 ]`

⇒ x = `2.65/0.53 and y = (-1.59)/(0.53)`

⇒ x = 5 and y = - 3