Solve a Simultaneous Equation with Examples

In this tutorial we will go through the simultaneous equations with examples. If there are two unknown variables, then we have to have two equations to find those two unknowns. Those kinds of equations called Simultaneous equations. Most of the time in grade 9 mathematics will cover the Simultaneous equations sections.

Simultaneous equations can be solve,

•     Elimination method
•     Substitution method

Elimination method

Ex:

4x + y = 9 ----------------- (1)
x – y = 1 ----------------- (2)

Step 1: Make the coefficients of the same in one of the variables in both equations. As you can see in the example variable “y” coefficients is 1 and -1. So we can simply eliminate “y” by adding two equations.

(1)    + (2)

4x + y + x – y = 9 + 1
5x = 10
x= 2

Now we can apply x in one of the equation (1 or 2), applying x for equation (1)

4 * 2 + y = 9
Y = 1

Now we can apply x and y in equations two and verify the results are fine.

Substitution method

This is more reliable method when solving hard questions.

Ex:

4x + y = 9 ----------------- (1)
x – y = 1 ----------------- (2)

Step 1: First define one variable from other variable in equation (1)

Y = 9 – 4x ----------------- (3)

Now apply equation (3) in equation (2)

x – y = 1
x – (9 – 4x) = 1
x - 9 + 4x = 1
5x = 10
x= 2

Apply x in equation (3)

y = 9 – 4*2
y = 1

Now verify your result applying in equation (1)

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