Question

Solve the system of equation algebraically: y = 2x2 - 5x + 10 and y = 2x + 5.

Answer 1

In order to solve the system of equations, let's equate both values of y and solve for x using the quadratic formula:

`\begin{gathered} 2x^2-5x+10=2x+5\\ \\ 2x^2-5x-2x+10-5=0\\ \\ 2x^2-7x+5=0\\ \\ a=2,b=-7,c=5\\ \\ x=(-b±√(b^2-4ac))/(2a)\\ \\ x=(7±√(49-40))/(4)\\ \\ x_1=(7+3)/(4)=(10)/(4)=(5)/(2)\\ \\ x_2=(7-3)/(4)=(4)/(4)=1 \end{gathered}`

Now, let's calculate the values of y for each value of x:

`\begin{gathered} x=(5)/(2):\\ \\ y=2x+5=5+5=10\\ \\ \\ \\ x=1:\\ \\ y=2x+5=2+5=7 \end{gathered}`

Therefore the solutions are (1, 7) and (5/2, 10).

Correct option: second one.