Answer:
The points of intersections are: <u>(1.5 , 1.25) and (4 , 0)</u>
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:
<u>(1.5 , 1.25) and (4 , 0)</u>
See the attached figure.
<u>Another solution:</u>
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:
so, a = 2 , b = -11 and c = 12
∴
∴ 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
<u>So, the solution are the points (4,0) and (1.5 , 1.25)</u>
