Solve: 7(y + 3) – 2(x + 2) = 14 , 4(y – 2) + 3(x – 3) = 2 [Simultaneous Linear Equations of two variables for Class 9 and 10]
7(y + 3) – 2(x + 2) = 14 —–(i)
4(y – 2) + 3(x – 3) = 2 ——(ii)
From equation (i) we get,
7(y + 3) – 2(x + 2) = 14
⟹ 7y +21 -2x-4=14
⟹ 7y-2x +17=14
⟹ 7y-2x = 14-17
⟹ 7y -2x= -3 ——-(iii)
from equation (ii) we get,
4(y – 2) + 3(x – 3) = 2
⟹ 4y-8+3x-9=2
⟹ 4y +3x -8 -9 = 2
⟹ 4y +3x – 17=2
⟹ 4y + 3x = 17+2
⟹ 4y +3x = 19 ——(iv)
Multiplying equation (iii) with 3 and equation (iv) with 2 then adding we get,
21y-6x + 8y+6x = -9 + 38
⟹ 29y = 29
⟹ y = $\frac{29}{29}$
⟹ y = 1
Substituting the value of y in equation (iii) we get ,
7(1) -2x= -3
⟹ 7-2x = -3
⟹ 7+3 =2x
⟹ 2x = 10
⟹ x = $\frac{10}{2}$
⟹ x = 5
∴ Required Solution is x = 5 and y =1