Question

Решите x^2-y^2=91 и 13x-7y=6

Answer 1

Какой класс?

Просто не знаю какой класс,я бы решила.

Answer 2

To solve the system of equations:

1. x^2 - y^2 = 91 ........(Equation 1)
2. 13x - 7y = 6 ........(Equation 2)

We can use the method of substitution or elimination to find the values of x and y.

Method 1: Substitution

Step 1: Solve Equation 1 for x^2: x^2 = y^2 + 91

Step 2: Substitute the expression for x^2 from Step 1 into Equation 2: 13(y^2 + 91) - 7y = 6

Step 3: Expand and simplify the equation: 13y^2 + 1183 - 7y = 6

Step 4: Move all terms to one side to form a quadratic equation: 13y^2 - 7y + 1183 - 6 = 0

Step 5: Combine like terms: 13y^2 - 7y + 1177 = 0

Now we have a quadratic equation in terms of y. We can solve this quadratic equation to find the values of y.

Step 6: Solve the quadratic equation. There are a couple of ways to do this. One way is to use the quadratic formula: y = (-b ± √(b^2 - 4ac)) / 2a

where a = 13, b = -7, and c = 1177

y = [7 ± √((-7)^2 - 4 * 13 * 1177)] / (2 * 13) y = [7 ± √(49 - 61084)] / 26 y = [7 ± √(-61035)] / 26

Since the discriminant (b^2 - 4ac) is negative, the solutions for y are complex. We can stop here, and there are no real solutions for y.

Therefore, the system of equations has no real solutions.

Method 2: Elimination

We can try using the method of elimination to solve the system.

Step 1: Multiply Equation 1 by 7 and Equation 2 by y to make the coefficients of y^2 equal: 7(x^2 - y^2) = 7 * 91 y(13x - 7y) = y * 6

Simplified: 7x^2 - 7y^2 = 637 ........(Equation 3) 13xy - 7y^2 = 6y ........(Equation 4)

Step 2: Now subtract Equation 4 from Equation 3 to eliminate y^2: (7x^2 - 7y^2) - (13xy - 7y^2) = 637 - 6y

Simplified: 7x^2 - 13xy = 637 - 6y

Step 3: Bring all terms to one side to form a quadratic equation: 7x^2 - 13xy + 6y - 637 = 0

Now we have a quadratic equation in terms of x. However, it is quite complex, and it seems that the previous method led us to the fact that there are no real solutions for y. Thus, the system does not have real solutions.

In conclusion, the system of equations x^2 - y^2 = 91 and 13x - 7y = 6 does not have any real solutions.