If you happen to be viewing the article An Introduction to Linear Equations? on the website Math Hello Kitty, there are a couple of convenient ways for you to navigate through the content. You have the option to simply scroll down and leisurely read each section at your own pace. Alternatively, if you’re in a rush or looking for specific information, you can swiftly click on the table of contents provided. This will instantly direct you to the exact section that contains the information you need most urgently.
The mathematical expressions of variables and constants along with the mathematical operations form an equation of the highest degree one. When plotted on a graph, a linear equation is an algebraic equation between variables that produces a straight line. A linear equation of one variable is of the form ax + b = 0 where x is the variable. Linear equations of two variables are of the form ax + by + c = 0 where x and y are the two variables and c is the constant. A pair of linear equations can be solved and represented using two basic methods: the graphical method and the algebraic method. In this article, we are going to learn about solving linear equations graphically.
Examples of Linear Equations
Contents
System of Linear Equations
A group of more than one linear equation is commonly known as a system of linear equations. For solutions, we can solve the system of linear equations graphically.
Solving Linear Equations in Two Variables
The solution to linear equations comes in a pair (x, y), one value for the variable x and one value for the variable y. Thus, the solutions for any linear equation in two variables in the form ax+by-c = 0 represent a particular point on the cartesian plane. The graph of a linear equation is always a straight line, no matter what the solutions are.
System of Linear Equations
How to Plot the Equations on a Graph
One Solution
Many Solution
No Solution
Solved Example
1. Check whether the equation $y = 5x + 4$ is linear or not.
Ans: An equation is considered linear if it is in the form of $y=m x+b$ where $mathrm{m}$ is the slope of the equation and $mathrm{b}$ is the $mathrm{y}$-intercept.
Here, $x$ can only be to the power of one.
Since $y = 5x + 4$ is in the form of $y=m x+b$ and x is having power 1. Therefore, the equation is linear.
2. Check whether the equation $y=3 x^2+1$ is linear or not.
Ans: Here, the power of x is more than 1. And for linearity, the power should be 1. Hence, the given equation is not linear.
3. What are the variable and contents in the given equation: $dfrac{1}{sqrt{2+x}}=1$
Ans:
Practice Questions
1. Check whether the equation $y = 9x + 10$ is linear or not.
Ans: Linear
2. Check whether the equation $y=2 x^5+10$ is linear or not.
Ans: Not Linear
3. Check whether the equation $y=4 x^2+ z$ is linear or not.
Ans: Not Linear
Summary
A linear equation is in the form of ax+by+c=0, where a and b are not equal to zero. A linear equation in two variables is an equation that contains two variables (x, y) and the highest degree of the equation is 1. A group of more than one linear equation is known as a system of linear equations. The solution to a system of linear equations in two variables can be found by solving the system graphically. To solve it graphically, the equations have to be graphed individually and then their point(s) of intersection determines the common solution.
Thank you so much for taking the time to read the article titled An Introduction to Linear Equations written by Math Hello Kitty. Your support means a lot to us! We are glad that you found this article useful. If you have any feedback or thoughts, we would love to hear from you. Don’t forget to leave a comment and review on our website to help introduce it to others. Once again, we sincerely appreciate your support and thank you for being a valued reader!
Source: Math Hello Kitty
Categories: Math
