Simultaneous equation is a group of equations that is composed of different variables. When you encounter these equations, you tend to be overwhelmed by the variables you see. However, when you look at it closely, simultaneous equations, like any other math problems, have steps and procedures we can follow to solve it easily.

Substitution Method

This method is often used in algebraic equations. We just solve one of the equations and find the value of one variable then we substitute it with the second equation to get both equivalents.

Example:

X + y = 28

2x – y = -4

You see, there are 2 variables that need to be solved. We take the first equation.

X + y = 28

X + y – y = 28 –y

X = 28 –y

Now, we have the value of x in terms of y. We can now then substitute it with the second equation

2x – y = -4

2*(28 –y) – y = -4

56 – 2y – y = -4

56 – 3y = -4

56 – 3y + 3y = -4 + 3y

56 = -4 + 3y

-4 + 3y = 56

-4 + 4 + 3y = 56 + 4

3y = 60

3y/3 = 60/3

Y = 20

Now that the real value for y is solved, we can now solve for the x.

X = 28 – y

X = 28 – 20

X = 8

Therefore, the value of x = 8 and the value of y = 20

Addition Method

Now we’ll use the addition method and take the same sample equation above.

X + y = 28

2x – y = -4

As the method suggest we just add the two equations. For the example above, we can eliminate the y.

X + y = 28

+ 2x – y = -4

3x = 24

3x/3 = 24/3

X = 8

Now that we know the value of x. We can use it to solve for y.

X + y = 28

8 + y = 28

8 – 8 + y = 28 – 8

Y = 20