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Math: Linear Equations - Tutorial
This section will cover the fundamentals and rules of linear equations in two variables.
Linear Equations in One Variable
The following is a linear equation in one variable. Notice the one variable x.
Example: x + 4 = 9
Solve for x by subtracting 4 from both sides.
Linear Equations in Two Variables
The following is a linear equation in two variables.
Example 1: x + y = 5
The equation is neither true nor false.
To solve the equation:
- Put in values for x and y.
- Arrange the equation to solve for x.
- Solve for y.
An easy way to do this would be to select some numbers and put them in table form.
Notice that the values for x and y all equal 5.
Plot the points on the graph.
Notice how the points fall on a line. A linear equation has the word line inside of its name.
Example 2: y = -4x
Choose any number for the value of x.
Let's choose the number, x = 2, x = 3, and x = 4.
Now solve for y.
Solving Linear Equations
Example 1: y - 3x = 2
In order to solve this equation, you will have to know the value to at least one of the variables. To do this, choose any number for x.
x = 4 (any number will work)
Rearrange the equation to solve for y, by adding 3x to both sides.
Plug 4 into the variable x.
This time, we'll try the number 3.
x = 4
x = 3
Choose other numbers to create a table of solutions.
Plot your points.
Example 2: y = 3
The y-coordinate is 3. Therefore, all of the points will be plotted 3 spaces above the x-axis.
More About Linear Equations
The relationship between x and y has to be to the first power, in order to be linear.
Substitute the values of x to get the value of y.
The following are not considered linear equations:
- Variables cannot be multiplied 6xy + y.
- The variable cannot be powered by an exponent other than 1.
- Variables cannot be divided.
- There can be no square root of a variable.
If all of the solutions for an equation were plotted on a coordinate plane, the line would be infinitely long.
4x
6y
1.
2.
3.
4.
Check your answer by plugging the solution back into the problem to see if it is correct.
The answer is correct.
