How do you know when an equation has infinitely many solution and when an equation has no solution?
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The issue is not when an equation has ... but when a system of equations has an infinite number of solutions, no solution,or a single solution.
TAke two lines:
y=m1* x + b1 and
y=m2*x+b2
If m1=m2, the lines are parallel, never intersect, and have no common points. It is said to have"no solution"
IF m1=m2 and b1=b2, the lines are the same, so have an infinite number of "solutions"
If m1 doesn not equal m2, the lines have a single solution.
To determine whether an equation has infinitely many solutions or no solution, you need to analyze the properties of the equation. Here are the steps to identify each case:
1. Infinitely Many Solutions:
- In an equation, if both sides are equal for any value of the variable(s) involved, it implies that the equation has infinitely many solutions.
- To confirm this, simplify the equation and see if any of the variables cancel out, resulting in a statement that holds true regardless of the values assigned to the variables.
2. No Solution:
- In an equation, if both sides are not equal, no matter what values you assign to the variable(s), it means that the equation has no solution.
- One method to identify no solution is to simplify the equation and observe if any contradictory statement arises.
- Additionally, you may also encounter situations where variables cancel out, resulting in a contradiction or an identity that cannot be solved.
Remember, these steps are general guidelines, and the specific method of identifying solutions may vary depending on the type and complexity of the equation.