Question

Solve the pair of equations by cross-multiplication method:

7(y + 3) - 2(x + 2) = 14; 4(y - 2) + 3( x - 3) = 2​

Answer 1

7y+21-2x-4=14

7y-2x=14-21+4

7y-2x=-3

Answer 2

Answer:

7(y+3)-2(x+2) = 14

7y+21-2x-4 = 14

7y-2x+17 = 14

7y-2x = -3

7y-2x+3 = 0

-2x+7y+3 = 0----------(1)

4(y-2)+3(x-3) = 2

4y-8+3x-9 = 2

4y+3x-17 = 2

4y+3x = 19

4y+3x-19 = 0

3x+4y-19 = 0--------------(2)

from (1) , a1 = -2 , b1 = 7 , c1 = 3

from (2) , a2 = 3 , b2 = 4 , c2 = -19

Using cross-multiplication method

x y 1

—————— = —————— = ——————

b1c2 - b2c1 c1a2 - c2a1 a1b2 - a2b1

x y 1

——————— = —————— = —————

(7)(-19)-(4)(3) (3)(3)-(-19)(-2) (-2)(4)-(3)(7)

x y 1

—————— = —————— = ——————

-145 -29 -29

x 1

---------- = ----------

-145 -29

-29x = -145

x = 5 --------------------(3)

y 1

---------- = --------

-29 -29

-29y = -29

y = 1 --------------------(4)

Hence x = 5 and y = 1

I made this answer by using so much of my time... ☹️