3. Solve the following pair of linear equations by the substitution and cross-multiplication methods:
8x +5y = 9
3x +2y = 4
8x +5y = 9 ... (i)
3x +2y = 4 ... (ii)
From equation (ii), we get
x = 4-2y/3 ... (iii)
Putting this value in equation (i), we get
8(4-2y/3) + 5y = 9
32 - 16y +15y = 27
-y = -5
y = 5 ... (iv)
Putting this value in equation (ii), we get
3x + 10 = 4
x = -2
Hence, x = -2, y = 5
By cross multiplication again, we get
8x + 5y -9 = 0
3x + 2y - 4 = 0
x/-20-(-18) = y/-27-(-32) = 1/16-15
x/-2 = y/5 = 1/1
x/-2 = 1 and y/5 = 1
x = -2 and y = 5
