Solving 2 Linear Simultaneous Equations

Solve the following:

5x - 3y = 14

2x - 7y = -6

Step 1: Label the 2 simultaneous equations 1 and 2:

1. 5x - 3y = 14

2. 2x - 7y = -6

Step 2: Make the numbers in front of both x terms OR y terms the same (as both numbers in front of the x terms are positive it is easier to do this for x terms)

1. (x all numbers by 2) 10x - 6y = 28

2. (x all numbers by 5) 10x - 35y = -30

Step 3: Calculate 1. - 2. to remove all x`s, to leave an equation just for y

10x - 6y = 28

-

10x - 35y = -30

=

0x + 29y = 58

29y = 58

Step 4: Work out what y is

29y = 58

y = 58 29

y = 2

Step 5: Sub y = 2 into 1. (One of the original equations, doesn`t matter which)

5x - (3 2) = 14

5x - 6 = 14

5x = 20

x = 20 5

x = 4

Step 6: Sub answers (x=4 and y=2) back into 2. (the other equation). If the LHS = RHS then we know we have the right answers

(2 4) - (7 2) = -6

8 - 14 = -6

As the LHS = RHS, x=4 and y=2 are our answers