Final answer:
The correct answer is option A: Both Equation 1 and Equation 2 have exactly one solution when solved. Equation 1 simplifies to x = 4/3, and Equation 2 simplifies to x = 6.71, demonstrating that each linear equation has a unique solution.
Step-by-step explanation:
The correct answer is option A: Equation 1 and Equation 2 have the same number of solutions. Both equations given are linear equations, meaning they will each have exactly one solution.
Let's solve Equation 1: 15x - 61 = -41. To find the value of x, we add 61 to both sides of the equation, getting 15x = 20. Then we divide both sides by 15 to solve for x, resulting in x = 20/15, which simplifies to x = 4/3, or approximately 1.333.
Now let's solve Equation 2: 17x + 13 = 127. We subtract 13 from both sides to get 17x = 114. We then divide both sides by 17, resulting in x = 114/17, which simplifies to x = 6.71.
Therefore, Equation 1 and Equation 2 each have one unique solution.
To solve Equation 1, you can start by adding 61 to both sides of the equation to isolate the variable: 15x = -41 + 61, which simplifies to 15x = 20. Then, divide both sides of the equation by 15 to solve for x: x = 20/15, or x = 4/3.
To solve Equation 2, start by subtracting 13 from both sides of the equation: 17x = 127 - 13, which simplifies to 17x = 114. Then, divide both sides of the equation by 17 to solve for x: x = 114/17.
Comparing the solutions, Equation 1 has a solution of x = 4/3, while Equation 2 has a solution of x = 6. Since the two equations have different solutions, the number of solutions cannot be determined.