Question

WILL GIVE 20 POINTS

The graph shows the system ​ {y=−x+2y=−x2+x+1 .​

Which ordered pair is the solution of the system?



​ (1, 1)

​ (1, 2) ​ ​

(0, 2)

​ (0, 1) ​

Answer 1

Option 1st is correct

(1, 1) ordered pair is the solution of the system

Explanation:

Given the system of equation:

`y = -x+2` ....[1]

`y=-x^2+x+1` ....[2]

Equate the equation [1] and [2] we have;

`-x+2=-x^2+x+1`

Add x to both sides of an equation:

`2=-x^2+2x+1`

Subtract 2 from both sides we have;

`0= -x^2+2x-1`

We can write this as:

`x^2-2x+1=0`

Using perfect square:

`(x-a)^2 = x^2-2ax+a^2`

⇒We can write the equation as:

`x^2- 2 \cdot x+1^2=0`

then;

`(x-1)^2 = 0`

⇒
`x-1 = 0`

Add 1 to both sides we have;

x =1

Substitute value of x in [1] we have;

`y = -1+2`

⇒
`y =1`

Solution for the given system of equation = (1, 1)

Also:

Graphically you can see that a line
`y = -x+2` intersect the graph
`y=-x^2+x+1` 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)