System of linear equations Class 12 Math Notes | Exercise-5.1 ( NEW CURRICULUM)

Class 12 Mathematics Notes has been updated according to the latest syllabus of 2080. It means the solution of system of linear equations chapter provided in this channel contains all the new exercise that has recently been updated. Now you don’t need to go anywhere searching for the notes of system of linear equations because we are here to serve you.
A fascinating topic! " System of linear equations"
In mathematics, a system of linear equations is a set of two or more equations in which each equation is a linear equation. A linear equation is an equation in which the highest power of the variable(s) is 1. For example, 2x + 3 = 5 and x - 2 = 0 are linear equations.
When we have a system of linear equations, we can use matrices to solve them. A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. In the context of linear equations, a matrix represents the coefficients of the variables in the equations.
Let's consider a simple system of two linear equations:
ax + by = c
dx + ey = f
where a, b, c, d, e, and f are constants, and x and y are variables.
To represent this system as a matrix, we can write:
| ax + by = c |
| dx + ey = f |
This matrix has two rows and two columns. The coefficients of the variables x and y are arranged in columns, and the constants c and f are arranged in rows.
Now, let's talk about intersecting, parallel lines, and coincident lines.
*Intersecting Lines:*
When two lines intersect, they meet at a single point. In the context of linear equations, this means that the system has a unique solution. The point of intersection is the value of x and y that satisfies both equations.
For example:
2x + 3y = 7
x + 2y = 3
We can solve this system using matrix methods (more on that later). The solution is x = 1 and y = 1. This means that the two lines intersect at the point (1, 1).
*Parallel Lines:*
When two lines are parallel, they never intersect. In the context of linear equations, this means that the system has no solution or infinitely many solutions.
For example:
2x + 3y = 7
2x + 3y = 10
These two lines are parallel because they have the same slope (rise over run). The system has no solution because there is no point where both lines meet.
*Coincident Lines:*
When two lines are coincident, they are actually the same line. In the context of linear equations, this means that the system has infinitely many solutions.
For example:
x + y = 2
x + y = 2
These two lines are coincident because they represent the same equation. The system has infinitely many solutions because every point on the line satisfies both equations.
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System of linear equations Class 12 Mathematics Notes | Exercise - 5.1 ( NEW CURRICULUM)