A linear equation with one variable is an algebraic equation with one solution. The linear equation x + y = 5 has many solutions. The value of x could be 2 and y could be 3, x could be 1 and 4, and x could be 5 and y could be 0. These all satisfy the equation. However, the linear equation x + 1 = 2 has only one solution. The value of x must be 1.
Let us look at a few linear equations. Here are five examples:
x + 6 = 10
3x + 2 = 17
y - 3 = 15
4x + 4 = 8
x + x + 3 = 7
The linear equation can be solved by putting the variable on one side of the equation and the numerical value on the other. The equations can be solved as follows:
x + 6 = 10
x = 10 - 6
x = 4
3x + 2 = 17
3x = 17 - 2
3x = 15
x = 5
y - 3 = 15
y = 15 + 3
y = 18
4x + 4 = 8
4x = 8 - 4
4x = 4
x = 1
x + x + 3 = 7
2x + 3 = 7
2x = 7 - 3
2x = 4
x = 2
Linear equations with one variable have only one solution. The variable is often represented by x or y, but other letters such as a and b are also common. To solve linear equations, the variable is placed on one side of the equation and the numerical value on the other.
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