Worksheet on Simultaneous Linear Equations

Practice each pair of the equation problems from the worksheet on simultaneous linear equations with the two variables and two linear equations. Solving simultaneous linear equations with two variables by using the method of substitution to solve each pair of the equations and also solve the equations by using the method of elimination.



1. Use the method of substitution to solve each other of the pair of simultaneous equations:

  (a) x + y = 15                  x - y = 3
  (b) x + y = 0                    x - y = 2
  (c) 2x - y = 3                 4x + y = 3
  (d) 2x - 9y = 9               5x + 2y = 27
  (e) x + 4y = -4               3y - 5x = -1
  (f) 2x - 3y = 2                 x + 2y = 8
  (g) x + y = 7                  2x - 3y = 9
  (h) 11y + 15x = -23        7y - 2x = 20
  (i) 5x - 6y = 2                6x - 5y = 9


2. Solve each other pair of equation given below using elimination method:

  (a) x + 2y = -4                        3x - 5y = -1
  (b) 4x + 9y = 5                      -5x + 3y = 8
  (c) 9x - 6y = 12                      4x + 6y = 14
  (d) 2y - (3/x) = 12                   5y + (7/x) = 1
  (e) (3/x) + (2/y) = (9/xy)       (9/x) + (4/y) = (21/xy)
  (f) (4/y) + (3/x) = 8             (6/y) + (5/x) = 13
  (g) 5x + (4/y) = 7                    4x + (3/y) = 5
  (h) x + y = 3                         -3x + 2y = 1
  (i) -3x + 2y = 5                       4x + 5y = 2


3. Solve the following simultaneous equations:

  (a) 3a + 4b = 43                      -2a + 3b = 11
  (b) 4x - 3y = 23                      3x + 4y = 11
  (c) 5x + (4/y) = 7                    4x + (3/y) = 5
  (d) 4/(p - 3) + 6/(q - 4) = 5       5/(p - 3) - 3/(q - 4) = 1
  (e) (l/6) - (m/15) = 4               (l/3) - (m/12) = 19/4
  (f) 3x + 2y = 8                        4x + y = 9
  (g) x - y = -1                         2y + 3x = 12
  (h) (3y/2) - (5x/3) = -2           (y/3) + (x/3) = 13/6
  (i) x - y = 3                           (x/3) + (y/2) = 6
  (j) (2x/3) + (y/2) = -1             (-x/3) + y = 3
  (k) 5x + 8y = 9                       2x + 3y = 4
  (l) 3 - 2(3a - 4b) = -59            (a - 3)/4 - (b - 4)/5 = 2¹/₁₀


Answers for the worksheet on simultaneous linear equations are given below to check the exact answers of the above questions on system of linear equations.

Answers:

1. (a) x = 9, y = 6
(b) x = 1, y = -1
(c) x = 1, y = -1
(d) x = 261/49, y = 9/49
(e) x = -8/23, y = -21/23
(f) x = 4, y = 2
(g) x = 6, y = 1
(h) x = -3, y = 2
(i) x = 4, y = 3

2. (a) x = -2, y = -1
(b) x = -1, y = 1
(c) x = 2, y = 1
(d) x = -1/2, y = 3
(e) x = 3, y = 1
(f) x = 1/2, y = 2
(g) x = -1, y = 1/3
(h) x = 1, y = 2
(i) x = -21/23, y = 26/23

3. (a) a = 5, b = 7
(b) x = 5, y = -1
(c) x = -1, y = 1/3
(d) p = 5, q = 6
(e) l = -2, m = -65
(f) x = 2, y = 1
(g) x = 2, y = 3
(h) x = 141/38, y = 53/19
(i) x = 9, y = 6
(j) x = -3, y = 2
(k) x = 5, y = -2
(l) a = 5, b = -4



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Worksheet on Simultaneous Linear Equations

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