The number of solutions to a linear equation depends on the specific characteristics of the equation.
In general, a linear equation will either have no solutions, one unique solution, or infinite solutions.
- If the equation is inconsistent, meaning the left and right sides of the equation do not equal and cannot be made equal by manipulating the variables, then there are no solutions. For example, the equation 2x = 5 has no solution because it is impossible for any value of x to make the equation true.
- If the equation is consistent but dependent, meaning the left and right sides of the equation are equal but the variables can take on any value, then there are infinite solutions. For example, the equation 2x = 2 has infinite solutions because any value of x makes the equation true.
- If the equation is consistent and independent, meaning the left and right sides of the equation are equal and there is only one specific solution for the variables, then there is one unique solution. For example, the equation 2x = 6 has one unique solution because only x = 3 satisfies the equation.
To determine the number of solutions, you may need to simplify or manipulate the equation to identify its characteristics.
Solving linear equations
How many solutions?
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