The document describes how to solve simultaneous equations using non-graphical methods. It involves numbering the equations, eliminating one of the unknowns by combining the equations, solving for the eliminated unknown, and then substituting back into one of the original equations to solve for the other unknown. Several examples are provided showing the steps of eliminating an unknown through addition or changing coefficients to match, then solving for the unknowns.

1. How to solve simultaneous equations using non-graphical
methods.

2. 6x + y = 15
4x + y = 11
Step 1 – Number the
equations(1)
(2) Step 2 – Eliminate one
of the unknowns
2x = 4 Step 3 – Work out the
unknown
x = 2
Step 4 – Using the value
of x in equation 1 or 2
find the value of y.
6 + y = 15x× 2
12 + y = 15
y = 3

3. 3x + 4y = 17
x + 4y = 3
Step 1 – Number the
equations(1)
(2) Step 2 – Eliminate one
of the unknowns
2x = 14 Step 3 – Work out the
unknown
x = 7
Step 4 – Using the value
of x in equation 1 or 2
find the value of y.
+ 4y = 3x7
y = -1
4y = -4

4. 3x +2y = 18
Step 1 – Number the
equations(1)
(2) Step 2 – Balance the
coefficient of one of
the unknowns
Step 3 – Eliminate
unknown by adding
Step 4 – Using the value
of x in equation 1 or 2
find the value of y.
2x - y = 5
4x -2y = 10 (3)
7x = 28
x = 4
- y = 5× 42 x
8 - y = 5 y = 3

5. How to solve simultaneous equations using the elimination
method where both equations need to be changed to obtain the
same coefficients in front of the unknown you wish to cancel

6. 4x +3y = 27
Step 1 – Number the
equations(1)
(2) Step 2 – Balance the
coefficients of one of
the unknowns in both
the equations
5x - 2y = 5
8x+6y = 54 (3)
15x- 6y= 15 (4)

7. 8x + 6y = 54
15x - 6y = 15
(3)
(4)
Step 3 – Eliminate one
of the unknowns
23x = 69
Step 4 – Work out the
unknown
x = 3 Step 5 – Using the value
of x in equation 1, 2, 3
or 4 find the value of y.
8 + 6y = 54x× 3
24 + 6y = 54
y = 56y = 30