Solve a system of two linear equations quickly

Solve a system of two linear equations quickly using this trick. It works 100% of the time and you waste no time, especially if you are taking an exam.

Trick #1:

Use when the system has the following format

x + y = e

x - y = f

x = (e + f)/2 and y = (e - f)/2

Example #1:

x + y = 18

x - y = 6

x = (18 + 6)/2 = 24/2 = 12

y = (18 - 6)/2 = 12/2 = 6

Example #2:

x + y = 9

x - y = 5

x = (9 + 5)/2 = 14/2 = 7

y = (9 - 5)/2 = 4/2 = 2

Trick #2:

Use when the system has the following format

ax + by = e

cx + dy = f

Example #3:

3x + y = 5

2x + 3y = 8

Here is how to find x in about 7 seconds

First rewrite everything without the variables. When looking for x, notice how we cross out the numbers that were attached to x to find the number on top. Cross multiply as shown. Before you multiply from bottom to top, put a subtraction sign.

Here is how to find y in about 7 seconds

Again, rewrite everything without the variables. When looking for y, cross out the numbers that were attached to y.