Simultaneous equations involve two variables, each of whose value must be found.
The following method, in which one equation is substituted into the other, works best when one equation contains a single letter on its own.
3x - 2y = 14
y - 2x = -9
3x - 2y = 14 (a)
y - 2x = -9 (b)
We find the equation with the single letter, i.e. (b), which has a single y in it.
We rearrange this to read y = ...
y = 2x - 9 (b)
Substitute (b) into (a).
Wherever we see a y in (a) we will replace it with (2x - 9), remembering the brackets.
3x - 2(2x - 9) = 14
Multiply out the brackets and solve.
Be careful with the double negative signs.
Notice that we now have an equation just in x.
3x - 4x + 18 = 14
-x + 18 = 14
-x = -4
x = 4
Now use (b) to determine y.
y = 2x - 9
When x = 4, this gives:
y = 2×4 - 9 = 8 - 9 = -1
y = -1
Check by putting this into the other equation (a) to get 3 × 4 - 2 × -1 = 12 + 2 = 14
Solution is x = 4, y = -1