ML Aggarwal Solutions Class 9 Math 5th Chapter Simultaneous Linear Equations Exercise 5.3
ML Aggarwal Understanding ICSE Mathematics Class 9 Solutions Fifth Chapter Simultaneous Linear Equations Exercise 5.3. APC Solution Class 9 Exercise 5.3.
(1) Solve the following systems of simultaneously linear equations by cross-multiplication method:
(i) 3x + 2y = 4
8x + 5y = 9
Solution:
(i) 3x + 2y = 4
Or, 3x + 2y – 4 = 0
∴ a1 = 3, b1 = 2, c1 = -4
8x + 5y = 9
Or, 8x + 5y – 9 = 0
a2 = 8, b2 = 5, c2 = -9
Cross multiplication,
(ii) 3x – 7y + 10 = 0
y – 2x = 3
Solution:
3x – 7y + 10 = 0, y – 2x = 3
Or, -2x + y – 3 = 0
a2 = -2, b2 = 1, c2 = -3
a1 = 3, b1 = -7, c1= 10
Cross Multiplication,
= x/11 = y/-11 = 1/-11
∴ x = -1, y = 1
(2) Solve the following pairs of linear equations by cross-multiplication method:
(i) x – y = a + b
ax + by = a2 – b2
Solution:
x – y = a + b
Or, x – y – (a + b) = 0
∴ a1 = 1, b1 = -1, c1 = – (a+b)
ax + by = a2 – b2
Or, ax + by – (a2 – b2) = 0
a2 = a, b2 = b, c2 = – (a2 – b2)
(ii) 2bx + ay = 2ab
bx – ay = 4ab
Solution:
2bx + ay = 2ab
Or, 2bx + ay – 2ab = 0
∴ a4 = 2b, b1 = a, c1 = -2ab
bx – ay = 4ab
Or, bx – ay – 4ab = 0
a2 = b, b2 = -a, b2 =-a, c2 = -4ab
Cross multiplying,