# 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.

Notice that the number that you use to divide the number on top is always the same.

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