Select the correct answer from each drop-down menu.y= x2 - 6x + 82y + x = 4The pair of points representing the solution set of this system of equations isandResetNext
Accepted Solution
A:
Answer:The points of intersections are: (1.5 , 1.25) and (4 , 0)Step-by-step explanation:Given:y = x² - 6x + 8 ⇒ (1)2y + x = 4 ⇒ (2)And required the solution of the system of equations.By graphing the system of equations, the points of intersections are:(1.5 , 1.25) and (4 , 0)See the attached figure.Another solution:By substitution of y from the second equation at the first equation.From (1) ⇒ y = 0.5 (4-x)At (2): and solve for x0.5 ( 4 - x ) = x² - 6x + 8 ⇒ multiply both sides by 24 - x = 2x² - 12x + 162x² - 12x + 16 + x - 4 = 02x² - 11x + 12 = 0The general solution of the quadratic equation: [tex]x = \frac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]so, a = 2 , b = -11 and c = 12∴[tex]x=\frac{-(-11) \pm \sqrt{(-11)^2-4*2*12} }{2*2}=\frac{11 \pm \sqrt{25} }{4} =\frac{11 \pm 5}{4} \\x = \frac{11+5}{4} = \frac{16}{4}=4\\ OR \ x = \frac{11-5}{4}=\frac{6}{4}=1.5\\[/tex]∴ at x = 4 ⇒ y = 0.5 (4-x) = 0.5 * 0 = 0And at x = 1.5 ⇒ y = 0.5 (4-x) = 0.5 * ( 4 - 1.5 ) = 0.5 * 2.5 = 1.25So, the solution are the points (4,0) and (1.5 , 1.25)