• In an equation, such as y = 3x – 4, the unknowns x and y are called variables.
• Simultaneous linear equations can be solved algebraically; either by substitution or by elimination.
• Simultaneous linear equations can also be solved graphically by drawing the graphs of the two equations on the same axes; their point of intersection gives the solution.

Examples

1. Solve the equations:
   3a + b = 10
   2a + 4b = 0
   • 3a + b = 10       – (i)
     2a + 4b = 0       – (ii)
   • from (i), b = 10 – 3a       – (iii)
   • Substitute (10 – 3a) for b in (ii): 2a + 4(10 – 3a) = 0
   • Clear the brackets: 2a + 40 – 12a = 0
   • Collect like terms: 2a – 12a = -40
   •                                    -10a = -40
   • ∴ a = 4
   • Substitue a = 4 in (iii): b = 10 – (3 × 4)
   •                                         b = 10 – 12
   • ∴ b = -2
   • Therefore, a = 4, and b = -2
2.  Solve the equations
   3f = 4 – 4e
   2e = 5f + 15
   • 3f = 4 – 4e        – (i)
     2e = 5f + 15     – (ii)
   • Arrange the equations so that the unknowns are in alphabetical order on the LHS and the numbers are on the RHS:
   • 4e + 3f = 4       – (iii)
     2e – 5f = 15      – (iv)
   • Multiply (iv) by 2: 4e – 10f = 30       – (v)
   • Subtract (v) from (iii) to eliminate terms in e: 13f = -26f
     ∴ f = -2
   • Substitute -2 for f in (ii): 2e = 5(-2) + 15
   •                                                2e = -10 + 15
   •                                                2e = 5
   • ∴ e = 2¹/₂