21.3 Solving linear equations with two unknowns by trial and improvement and by elimination
By the end of this section you should be able to:
● solve a pair of simultaneous equations using trial and improvement
● solve simultaneous equations by elimination
Method 2: Solving simultaneous equations using trial and improvement Any equation can be solved by trial and improvement.
Solving simultaneous equations by trial and improvement Estimate a solution for the two variables.
1
2 3 4
Substitute these estimates into one of the equations to determine whether your estimate is too high or too low to allow the left-hand side equal the right-hand side.
Refi ne your estimate and repeat the process until you fi nd two values such that the left-hand side equals the right-hand side.
Check the two variables that satisfy the 1st equation also satisfy the 2nd equation. If this is not the case, repeat the process until it is the case.
Worked example 1
Solve the simultaneous equations 3x + y = 11 and 2x + y = 8 using the trial and improvement method. Show all your workings.
Solution 3x + y = 11
2x + y = 8 3x + y = 11 ✗
(equation A) (equation B)
The symbol ≠ means ‘not equal to’
3x + y = 11 ✗ 3x + y = 11 ✓
2x + y = 8 (equation B)
Trial and improvement can be very time consuming. Furthermore, if you work with equations where the unknown is not a whole number, it will take a lot of time to fi nd the correct decimal. Therefore, it is not a method that we normally use.