Systems of Linear Equations

Linear equations are an essential part of chemical engineering. Linear equations are an important chapter for preparing for GATE exams. Having a greater understanding of linear equations leads to a boost in confidence and accuracy. Linear equations are composed of symbols, numbers, and variables. Linear equations have a special characteristic. Its highest power is 1 and anything more than that is not linear. Linear equations are algebraic expressions. It is associated with algebra. In the chemical engineering field, the understanding of chemical plants is essential. The operations design and ways of improving output are key elements of studying chemical engineering. 

Linear Equations

These computations serve in better functioning of calculations and help in dealing with complex situations. Linear equations are emphasised as accurate results are a necessity in chemical engineering. There are two types of linear equations:

• One variable linear equations

• Two variables

It is represented as:

Rx + L = 0

In this equation, three things are kept in mind:

• x is a variable that has to be determined

• R is a coefficient

• L is constant

The number of variables can increase. In the case of 2 variables, the linear equation is:

Rx + Ly = W

In this one, R, as well as L, are coefficients. W is a constant. 

What is a Linear Equation?

Linear equations are algebraic expressions. The section answers what is a linear equation. Students often get confused between an algebraic equation and a linear equation. That is when they ask, ‘what is a linear equation?’ Linear equations are simply algebraic expressions. Linear equations are composed of symbols, numbers, and variables. It is associated with algebra. Students also might ask, ‘what is a linear equation if it is not an algebraic equation?’ The answer is that it is a part of algebraic equations. The linear equation is a specific chapter of algebra. It is a type of algebraic equation. So, this was the discussion of the question of what is a linear equation. The key benefits are:

• Helps in modelling structures and plans

• Helps in designs

• Helps in operations processes

• Helps in test simulations

Linear Equation Definition

Linear equation definition helps students understand the topic better. For GATE preparations, algebra is a scary but necessary chapter to master. It can be done through practice. Practices can be done when the linear equation definition is understood. So, the linear equation definition is provided. It is an algebraic equation for a line. Its highest power is 1 and anything more than that is not linear. Here are some examples of linear equations:

• l = 2c + 1

• h/2 = 3 – d

• 5v = 6 + 3f

Here are some characteristics of linear equations according to the linear equation definition:

• The highest power is 1

• It is an equation of a straight line

• Square or cube roots are not included here

• Plotting linear equations will reveal a straight line on a graph

• Variables do not have exponents

System of Linear Equations

System of linear equations are of three major categories:

• Point slope [d – d1 = v (f – f1)]

• Slope intercept (d = vx + n)

• General (Bx + Ry + D = 0)

The system of linear equations also contains another feature. It serves as a function. In that case:

V = 2t – 3 is the same as f(c) = 2t – 3. 

Linear equations function can be further divided into:

• Constant Function

• Identity Function

Uses of Linear Equations

Linear equations are useful for solving problems. Following are the uses of linear equations:

• Conversions

• Linking variables

• Calculating rates

• Makingaccurate predictions

• Used in simulation and control tests

• Helps in operational processes

Conclusion

In the chemical engineering field, the understanding of chemical plants is essential. The operations design and ways of improving output are key elements of studying chemical engineering. Having a greater understanding of linear equations leads to a boost in confidence and accuracy. Algebra forms an important chapter of maths in chemical engineering. So, linear equations are essential for chemical engineering. These computations serve in better functioning of calculations and help in dealing with complex situations. Linear equations are emphasised as accurate results are a necessity in chemical engineering.