How do you solve the following simultaneous equation?

2x - 6y = 18

4x + 3y = 6

First, make either the x or y the same value by multiplying the equations. Let's choose x.

 

2x - 6y = 18      x2

4x + 3y = 6       x1

 

(+)4x - 12y = 36

(+)4x + 3y = 6

 

Now, we use the rule of 'same sign subtract', 'different sign add'. As the signs are the same in this example, we will subtract the equations.

-15y = 30

 

Now, we must divide both sides by -15 in order to isolate the y.

 

y = 30/-15

y = -2

 

We must then substitute the value for y into one of the equations to find x.

 

4x + 3y = 6     (substitute y = -2)

 

4x + 3(-2) = 6

 

4x - 6 = 6

 

Now we must add 6 to both sides to get the 4x on its own.

 

4x = 12

 

Then divide both sides by 4 to find the value of x.

 

x = 12/4

 

x = 3

 

We can then check our values (x = 3, y = -2) are correct by substituting them into the other equation.

 

4x + 3y = 6     (substitute x = 3, y = -2)

 

4(3) + 3(-2) = 6

 

12 - 6 = 6

 

6 = 6

 

This means that we successfully solved the simultaneous equation.