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The maximum power of a variable in a linear equation is always 1. It’s also known as a one-degree equation. We can represent a linear equation in one variable as Mx + N = 0. In the given equation, x is a variable, M is a coefficient, and N is a constant.
What does having a linear equation imply?
An equation with a maximum degree of one is known as a linear equation. This signifies that no variable in a linear equation has an exponent bigger than 1. The linear equation’s graph is always a straight line.A linear equation is an algebraic equation with an exponent of 1 for each component and a graph that always creates a straight line when graphed. Because of this it’s called a ‘linear equation’.There are two types of linear equations: one-variable and two-variable.
With the help of the examples below, we will learn how to recognise linear and nonlinear equations.
Equations | Linear or Nonlinear |
y = 8x – 9 | Linear |
y = x2 – 7 | Non-Linear, the power of the variable x is 2 |
√y + x = 6 | Non-Linear, the power of the variable y is 1/2 |
y + 3x – 1 = 0 | Linear |
Linear Equations in One Variable:
A linear equation in one variable is an equation with only one variable. It takes the shape Ax + B = 0, with A and B being any two real numbers and x being a single-valued unknown variable. It’s the most straightforward way of expressing a mathematical claim. This equation’s degree is always equal to one. Solving a one-variable linear equation is quite straightforward. The variables are separated and brought to one side of the equation, while the constants are combined and brought to the other side to discover the value of the unknown variable.
Example:
Solve the linear equation 3x + 6 = 18 in one variable.
To solve the given problem, we move the numbers to the right-hand side of the equation while keeping the variable on the left-hand side.
This is equivalent to 3x = 18 – 6. Then, when we solve for x, we get 3x = 12. Hence x = 12/3 = 4 .
Linear Equations in Two Variables:
Ax + By + C = 0 is a two-variable linear equation with A, B, and C as real integers and x and y as the two variables, each with a degree of one. Two linear equations with the same solution are known as simultaneous linear equations. 6x + 2y + 9 = 0 is a two-variable linear equation, for example.
Methods for solving linear equations in two variables include the graphical approach, substitution method, cross multiplication method, elimination method, and determinant method.
How to Solve Linear Equations?
An equation is a weighing balance with equal weights on both sides. If we add or subtract the same number from both sides of an equation, it still stays true. Multiplying or dividing the same integer on both sides of an equation is also valid. We obtain the value of the unknown variable by moving the variables to one side of the equation and the constant to the other. This is how you solve a linear equation with only one variable. Let’s look at an example to see how this works.
Solution of Linear Equations in Two Variables:
The graph illustrating the solution of linear equations in two variables, ax+by = c, shows that when the x-coordinate is multiplied by a and the y-coordinate is multiplied by b, the sum of these two values will be equal to c.There can be n number of solutions to a two-variable linear equation.
Example:
To find the solution to a linear equation in two variables, you’ll need to know two equations.
Consider for Example:
5x + 3y = 30
There are two variables in the equation above: x and y.The variables can be set to zero to display this equation graphically.
The value of y when we put x = 0 is
5x + 3(0) = 30
⇒ x = 6
when we put x = 0 the value of y is,
5 (0) + 3y = 30
⇒ y = 10
It is now evident that the two equations must first be found before the substitution strategy can be used to solve a linear equation in two variables.
Conclusion
We can use equations to solve challenges in our daily lives. In order to solve real-life problems, we regularly seek pre-algebra help. Pre-algebra principles are the fundamentals of mathematics. Computer chips are now found in all of the appliances we use on a daily basis, such as washing, dryers, automobiles, and backs.
