Lesson Notes By Weeks and Term v4 - SHS 1
APPLICATIONS OF ALGEBRA
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APPLICATIONS OF ALGEBRA
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Subject: Additional Mathematics
Class: SHS 1
Term: 1st Term
Week: 13
Grade code: 1.1.2.LI.1
Strand code: 1
Sub-strand code: 2
Content standard code: 1.1.2.CS.1
Indicator code: 1.1.2.LI.1
Theme: MODELLING WITH ALGEBRA
Subtheme: APPLICATIONS OF ALGEBRA
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This lesson introduces the powerful technique of solving systems of linear equations. In our daily lives in Ghana, we often face situations where we have several unknown quantities and several pieces of information relating them. For example, a market trader trying to determine the cost price of different items, or an entrepreneur calculating production costs. Algebra gives us a systematic way to model these situations and find the exact values of the unknowns. By learning to solve these systems, we are developing critical thinking and problem-solving skills that are valuable in science, engineering, economics, and even everyday decision-making.
What is a System of Linear Equations?
A linear equation is an equation whose graph is a straight line. It involves variables raised only to the power of 1 (e.g., `2x + 3y = 7`).
A system of linear equations is a collection of two or more linear equations involving the same set of variables. We try to find a single set of values for the variables that makes *all* the equations in the system true at the same time. This set of values is called the solution to the system. A system with two equations and two variables (like `x` and `y`) is called a 2x2 system. A system with three equations and three variables (like `x`, `y`, and `z`) is called a 3x3 system.
Today, we will learn two main algebraic methods: Substitution and Elimination.