Question

X-y=2
2x+3y=14
use the elimination method to solve the system of equations.

Answer 1

x=7, y=2. (7, 2).

Step-by-step explanation:

x-y=2

2x+3y=14

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x=y+2

2(y+2)+3y=14

2y+4+3y=14

5y+4=14

5y=14-4

5y=10

y=10/5

y=2

x=5+2=7

Answer 2

The asymptotes of the function f(x) = 7/(x^2 - 2x - 24) are located at x = 6 and x = -4.

Step-by-step explanation:

The function f(x) is a rational function, which means it's a fraction of two polynomials. The function has vertical asymptotes where the denominator (x^2 - 2x - 24) equals zero.

To find the asymptotes, set the denominator equal to zero and solve for x:

x^2 - 2x - 24 = 0

Factor the equation: (x - 6)(x + 4) = 0

Therefore, x = 6 and x = -4 are the roots of the denominator.

Since the denominator becomes zero at x = 6 and x = -4, these points represent vertical asymptotes where the function approaches positive or negative infinity.

Therefore, the function f(x) has asymptotes at x = 6 and x = -4.