Patterns Within Systems of Linear Equations

Jasmine Chai Grade 10 196298501 Patterns within systems of linear equations Systems of linear equations are a collection of linear equations that are related by having one solution, no solution or many solutions. A solution is the point of intersection between the two or more lines that are described by the linear equation. Consider the following equations: x + 2y = 3 and 2x – y = -4. These equations are an example of a 2×2 system due to the two unknown variables (x and y) it has. In one of the patterns, by multiplying the coefficient of the y variable by 2 then subtract the coefficient of x from it you will be given the constant.As a word equation it can be written like so with the coefficient of x as A and coefficient of y as B and the constant as C, 2B – Ax = C. This can be applied to the first equation (x + 2y = 3) as 2(2) – 1 = 3. To the second equation (2x – y = -4), it is -1(2) – 2 = -4. By using matrices or graphs, we can solve this system. Regarding other systems that also has such as pattern, it should also have the same solution as the two examples displayed.