system of equation

What is System of Equation?

A system of equations is when you have more than one algebraic equation that you need to solve at the same time. These equations usually have more than one variable (unknown), and you need to find the values of those variables that satisfy all the equations at once.

Simple Example

For example, let’s say there are two different kinds of fruit for sale at a store: apples and oranges. You know that you bought a total of 10 pieces of fruit and paid $12. You also know that each apple costs $1 and each orange costs $2. You can create a system of equations to figure out how many of each fruit you bought.

Equation 1: A + O = 10 (total pieces of fruit)
Equation 2: A + 2O = 12 (total cost)

Explanation

Now, you can solve these equations simultaneously to find out how many apples (A) and oranges (O) you bought.

In this case, you can solve the equation by eliminating one of the variables. You can multiply Equation 1 by 2 and subtract Equation 2 to eliminate the variable A:

2(A + O) – (A + 2O) = 20 – 12
2A + 2O – A – 2O = 8
A = 8

Now that you know A = 8, you can substitute this value back into Equation 1 to find O:

8 + O = 10
O = 2

So, you bought 8 apples and 2 oranges. That’s how you solve a system of equations!