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Drag the tiles to match each equation to its number of solutions. Each tile may be used only once.

2 Answers

7 votes

Final Answer:

- Equation 1: One solution

- Equation 2: Infinite solutions

- Equation 3: No solution

Step-by-step explanation:

Equation 1,
\(2x + 4 = 8\), is a linear equation with one variable and one solution. It can be solved by isolating the variable, yielding a unique solution. Equation 2,
\(3x - 2 = 3x - 2\), is an identity where both sides are equal regardless of the value of x. This indicates infinite solutions since any value for x satisfies the equation.

Equation 3,
\(5x + 7 = 5x + 9\), leads to a contradiction when simplified, implying no solution. This happens when the variable disappears, and the statement becomes false. In detail, subtracting 5x from both sides leaves 7 = 9, which is not a true statement. Therefore, the system has no solution.

In summary, Equation 1 has one solution due to its linear nature, Equation 2 has infinite solutions as an identity, and Equation 3 has no solution because it leads to a contradiction during the simplification process. The different outcomes highlight the diverse possibilities in systems of linear equations.

User Vad
by
8.4k points
1 vote

Answer:

1- one solution 2- many solutions 3- no solution

Step-by-step explanation:

User BruceHill
by
8.3k points

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