Linear equations can have one solution, no solution, or infinite solutions.
A linear equation has one solution when it is satisfied by exactly one value of the variable. – Example 1: 7x - 35 = 0 has one solution, x = 5.
A linear equation has no solution when it leads to a false statement that can't be true for any value of the variable. – Example 1: 7x - 35 = 5x + 2x - 27 has no solution.
– A linear equation has infinite solutions when it results in a true statement that is true for any value of the variable. – Example 1: 25x - 35 = 5(5x + 4) - 55 has infinite solutions.
– No solution occurs when the variable disappears during solving, and the equation becomes a false statement.
Students can practice their understanding by solving linear equations and identifying whether they have one solution, no solution, or infinite solutions.