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The system of equations is solved by substitution, expanding, simplifying, using the quadratic formula to find x values, and then substituting back into the equations to find the corresponding y values. The solutions are (3, 4) and (-4, -3).

The solution to the system of equations x + 2y = 5 and 3x - y = 1 is x = 1 and y = 2, found using the elimination method.

The solution for x in the equation involving fractions with (x-1) and (x+1) in the denominator is x = √2 and x = -√2.

The solution to the equation 3^(a^2 - 10a + 25)! = 729^4 is a = 3 or a = 7, found by equating exponents after expressing both sides with the same base and solving the resulting quadratic equation.

To find the difference between ba and ab, where a and b are digits, we analyze the units and hundreds digits, leading to the conclusion that the hundreds digit of the difference is 3.

The solution to the equation 4a³ = 2⁵ is a = 2.

The equation was solved by simplifying the square root, isolating the square root term, squaring both sides, moving all terms to one side, factoring out a common factor, and solving for x, resulting in two solutions: x = 0 and x = 16/81.

The solution to the equation 3^x = 1 and 3^y = 81 is x + y = 4.

By solving the system of equations x + y = 3 and x - y = 9, we find x = 6 and y = -3. Then, substituting these values into (x/y)^2, we get 4.

The total volume of infinitely many cubes with side lengths decreasing according to the sequence 1, 1/√2, 1/√3, ... is finite, while the total surface area is infinite.

The expression 2^(n+4) - 2(2^n) / 2(2^(n+3)) simplifies to 7/8.

The derivative of xy + sin(x) = e^y with respect to x is found using implicit differentiation, applying the product rule and chain rule, and solving for dy/dx.

The derivative of x² + y² = 25 with respect to x is -x/y.

The derivative of sin(2x² + 3x) is found using the chain rule, differentiating the outer sine function and the inner quadratic function separately, and then multiplying the results: cos(2x² + 3x) * (4x + 3).

The derivative of the function f(x) = 3x^2 - 4x + 7 is f'(x) = 6x - 4.

The problem involves finding the value of x in an expression where the greatest common factor (GCF) of two terms is given. The GCF is used to determine the value of x, but the problem cannot be solved without additional information about the variable y.

To find the area of the shaded region, subtract the area of a circle (formed by two semicircles) from the area of the enclosing rectangle.

The equation "\[\sqrt{(M-4)(M+4)} = 3\]" was solved by squaring both sides, expanding, simplifying, and taking the square root to find the solutions M = 5 and M = -5.

To find y when x = 4, substitute x = 4 into the equation y = 2x² - 3x + 1. Solving gives y = 21.

The limit of (1 + 1/x)^x as x approaches infinity is e.

The limit of sin(x)/x as x approaches 0 is 1, determined using L'Hôpital's rule.

The limit of (x² - 1) / (x - 1) as x approaches 1 is 2. This is found by factoring the numerator (difference of squares) and canceling the common factor of (x - 1).

The solution to the equation 25^x = 125 is x = 3/2. Squaring this value gives x^2 = 9/4.

The quadratic equation x^2 - x - 6 = 0 was solved by factoring. The solutions are x = 3 and x = -2.

The solution to 4 + 3 - 6 * (6 - 9) is 25.

The limit of (2x)/(x-7) as x approaches 7 from the right is positive infinity.

Solve the inequality 2x - 7 > 5. Find the solution to the inequality and learn how to isolate the variable. Answer: x > 6

Find the integral of x² + 3x - 2. Solution: (x³)/3 + (3x²)/2 - 2x + C

Calculate the definite integral of sin²(x) from 0 to π. Find the solution to this trigonometric integral problem, demonstrating the use of the identity sin²(x) = (1-cos(2x))/2. The answer is π/2.