Question

Solve, using cross-multiplication :
5x + 4y + 14 = 0
3x = -10 - 4y

Answer 1

Given equation are 5x + 4y + 14 = 0 and 3x = -10 - 4y
Comparing with a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, We have
a₁ = 5, b₁ = 4, c₁ = 14 and a₂ = 3, b₂ =  4, c₂ = 10

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 = `[ 4 xx 10 - 4 xx 14 ]/[ 5 xx 4 - 3 xx 4 ]  and  y = [ 14 xx 3 - 10 xx 5 ]/[ 5 xx 4 - 3 xx 4 ]`

⇒ x = `[ 40 - 56 ]/[ 20 - 12 ] and y = [ 42 - 50 ]/[ 20 - 12 ]`

⇒ x = ` -16/8 and y = -8/8`

⇒ x = -2 and y = -1