Use the drop-down menus to complete each equation so the statement about its solution is true.
No Solutions
One Solution
Infinitely Many Solutions
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To fill in the drop-down menus for each type of equation based on the solutions they provide, let’s go through the concepts:
1. No Solutions: This occurs when the equations are contradictory, meaning they represent parallel lines that never touch. For example, the equations (2x + 3 = 7) and (2x + 3 = 9) have no solutions.
2. One Solution: This occurs when the equations intersect at exactly one point. For example, the equations (x + 2 = 5) and (2x + 1 = 5) have one solution because they cross at a single point.
3. Infinitely Many Solutions: This happens when the equations are equivalent, meaning they represent the same line. For example, the equations (2x + 3 = 7) can be rewritten as (4x + 6 = 14) which gives infinitely many solutions.
When using drop-down menus, select the appropriate option based on the above definitions. If you have specific equations in mind, feel free to share, and I can help you determine the correct classifications!