Question

Select the correct answer. What is the solution set of 4x = y and 2x2 − y = 0? {(0.5, -0.5), (2, -8)} {(0, 0), (2, 8)} {(1.5, 2), (8, 2)} {(-1.5, -2), (2, 8)}

Answer 1

$\left\{\begin{array}{ccc}4x=y&(1)\\2x^2-y=0&(2)\end{array}\right\\\\/\text{substitute (1) to (2)/}\\\\2x^2-4x=0\\2x(x-2)=0\iff 2x=0\ \vee x-2=0\\\\x=0\ \vee\ x=2\\\\for\ x=0\to y=4\cdot0=0\\for\ x=2\to y=4\cdot2=8\\\\(0;\ 0);\ (2;\ 8)\\\\Answer:\ \{(0;\ 0);\ (2;\ 8)\}$