Table of Contents
What are Linear Equations in One Variable?
A linear equation in one variable is an equation that can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of a line is the rate of change of y with respect to x, and the y-intercept is the point at which the line crosses the y-axis.
Solving Linear Equations
A linear equation is an equation in which each term is a linear function of the variable. Linear equations can be written in the form y = ax + b, where a and b are constants and x is the variable. The graph of a linear equation is a straight line.
To solve a linear equation, you must first isolate the variable. To do this, you must use algebraic methods to get all the terms of the equation except for the variable on one side of the equation. Once the variable is isolated, you can solve for it using basic algebraic methods.
Steps – by – Step Solution for a Linear Equations in One Variable
Step 1:
The first step is to identify the equation that needs to be solved. In this example, the equation is y = 2x + 1.
Step 2:
The next step is to isolate the variable. In this example, that would mean solving for y. To do that, subtract 2x from both sides of the equation.
y = 2x + 1
y – 2x = 1
Step 3:
The last step is to solve for y. To do that, divide both sides of the equation by -2.
y – 2x = 1
y = -1/2x + 1
Solving Equations By Collecting Terms
To solve equations by collecting terms, we use the distributive property to combine like terms on each side of the equation.
For example, consider the equation
3x + 2y = 9
We can combine the 3x and 2y terms on the left side of the equation to get
3x + 2y = 9
3x = 9 – 2y
We can then solve for x by solving for y.
y = 9 – 3x
So, the solution to the equation is
x = 3
y = 6
