Lesson HOW MANY SOLUTIONS can there be in a linear equation?

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How many solutions can there be in a linear equation ax%2Bb=c, where c, b, and c are constants?

The first answer that leaps to mind is one solution. Usually, especially in regular school math, that is the case. But not always.

Case 1. One Solution


All linear equations ax+b=c where a is not equal to zero, have one solution:
x=%28c-b%29%2Fa

Case 2. No Solutions


A linear equation can have no solutions. Example: 0x + 1 = 2. Since 0x is always 0, and 0+1 = 1, we have an impossible equation 1=2. Any linear equation with no solution always has zero (0) as the coefficient before x.

Case 3. Infinitely many solutions


A linear equation can have infinitely many solutions. Example: 0x+4=4. Since 0x is always 0 regardless of x, any value of x satisfies this equation.

Conclusions


So, be careful with problems that reduce to a linear equation. Beware that they may have no solutions or an infinite number of solutions.
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