Precalculus, Chapter 7, 7.1, Section 7.1, Problem 55

Since the equations of the system are not transcendental equations, you may solve the system algebraically.
You need to use substitution method, hence, you may use the second equation to express x in terms of y, such that:
2x = 4y - 7 => x = (4y - 7)/2
Replacing (4y - 7)/2 for x in equation xy - 1 = 0 , yields:
((4y - 7)/2)*y - 1 = 0 => 4y^2 - 7y - 2 = 0
You may use quadratic formula, such that:
y_(1,2) = (7+-sqrt(49 + 32))/8
y_(1,2) = (7+-sqrt(81))/8
y_(1,2) = (7+-9)/8
y_1 = (7+9)/8 => y_1 = 2 => x_1 = 1/2
y_1 = (7-9)/8 => y_1 = -1/4 => x_2 = -4
Hence, evaluating the solutions to the given system, yields (1/2,2) and (-4,-1/4).