Answer:
Option 1st is correct
(1, 1) ordered pair is the solution of the system
Step-by-step explanation:
Given the system of equation:
[tex]y = -x+2[/tex] ....[1]
[tex]y=-x^2+x+1[/tex] ....[2]
Equate the equation [1] and [2] we have;
[tex]-x+2=-x^2+x+1[/tex]
Add x to both sides of an equation:
[tex]2=-x^2+2x+1[/tex]
Subtract 2 from both sides we have;
[tex]0= -x^2+2x-1[/tex]
We can write this as:
[tex]x^2-2x+1=0[/tex]
Using perfect square:
[tex](x-a)^2 = x^2-2ax+a^2[/tex]
⇒We can write the equation as:
[tex]x^2- 2 \cdot x+1^2=0[/tex]
then;
[tex](x-1)^2 = 0[/tex]
⇒[tex]x-1 = 0[/tex]
Add 1 to both sides we have;
x =1
Substitute value of x in [1] we have;
[tex]y = -1+2[/tex]
⇒[tex]y =1[/tex]
Solution for the given system of equation = (1, 1)
Also:
Graphically you can see that a line [tex]y = -x+2[/tex] intersect the graph [tex]y=-x^2+x+1[/tex] at a point (1, 1) which satisfy the given system of equations.
Therefore, the ordered pair is the solution of the system is, (1, 1)
