Question

Select the correct answer from each drop-down menu.

Answer 1

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 x

0.5 ( 4 - x ) = x² - 6x + 8 ⇒ multiply both sides by 2

4 - x = 2x² - 12x + 16

2x² - 12x + 16 + x - 4 = 0

2x² - 11x + 12 = 0

The general solution of the quadratic equation:

$x = \frac{-b \pm \sqrt{b^2-4ac} }{2a}$

so, a = 2 , b = -11 and c = 12

∴$x=\frac{-(-11) \pm \sqrt{(-11)^2-4*2*12} }{2*2}=\frac{11 \pm \sqrt{25} }{4} =\frac{11 \pm 5}{4} \\x = \frac{11+5}{4} = \frac{16}{4}=4\\ OR \ x = \frac{11-5}{4}=\frac{6}{4}=1.5$

∴ at x = 4       ⇒ y = 0.5 (4-x) = 0.5 * 0 = 0

And at x = 1.5 ⇒ y  = 0.5 (4-x) = 0.5 * ( 4 - 1.5 ) = 0.5 * 2.5 = 1.25

So, the solution are the points (4,0) and (1.5 , 1.25)