A2400 ch3a | Version 1.1 | September 2020
Solving linear simultaneous equations by
elimination
A LEVEL LINKS
Scheme of work: 1c. Equations – quadratic/linear simultaneous
Key points
• Two equations are simultaneous when they are both true at the same time.
• Solving simultaneous linear equations in two unknowns involves finding the value of each
unknown which works for both equations.
• Make sure that the coefficient of one of the unknowns is the same in both equations.
• Eliminate this equal unknown by either subtracting or adding the two equations.
Example 1 Solve the simultaneous equations 3x + y = 5 and x + y = 1
3x + y = 5
– x + y = 1
2x = 4
So x = 2
Using x + y = 1
2 + y = 1
So y = −1
Check:
equation 1: 3 × 2 + (−1) = 5 YES
equation 2: 2 + (−1) = 1 YES
1 Subtract the second equation from
the first equation to eliminate the y
term.
2 To find the value of y, substitute
x = 2 into one of the original
equations.
3 Substitute the values of x and y into
both equations to check your
answers.
