Question

Solve, using cross-multiplication :
4x + 3y = 17
3x - 4y + 6 = 0

Answer 1

Given equation are 4x + 3y = 17 and 3x - 4y + 6 = 0
Comparing with a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, We have

a1 = 4, b1 = 3, c1 = -17 and a2 = 3, b2 = - 4, c2 = 6

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 = `[ 3 xx 6 - ( - 4 ) xx ( - 17 )]/[ 4 xx (-4) - 3 xx 3 ]  and  y = [ - 17 xx 3 - 6 xx 4 ]/[ 4 xx ( - 4 ) - 3 xx 3 ]`

⇒ x = `[ 18 - 68 ]/[ - 16 - 9 ]  and y = [ - 51 - 24 ]/[ - 16 - 9 ]`

⇒ ` x = [ - 50 ]/[ - 25 ] and y = [ - 75 ]/[ - 25]`

⇒ x = 2 and y = 3.