Y= x2 − 6x + 8
2y + x = 4
the pair of points representing the solution set of this system of equations is

The two intersections are (3/2 , 5/4) and (4,0).

I put two ways to do it. You can pick your favorite of these are try another route if you like.

Step-by-step explanation:

The system is:

.

I don't know how good at factoring you are but the top equation consists of polynomial expression that has a factor of (x-4).  I see that if I solve 2y+x=4 for 2y I get 2y=-x+4 which is the opposite of (x-4) so -2y=x-4.

So anyways, factoring x^2-6x+8=(x-4)(x-2) because -4+(-2)=-6 while -4(-2)=8.

This is the system I'm looking at right now:

I'm going to put -2y in for (x-4) in the first equation:

So one solution will occur when y is 0.

Now assume y is not 0 and divide both sides by y:

Distribute:

Subtract 4 on both sides:

Divide both sides by -2:

Now let's go back to one of the original equations:

2y=-x+4

Divide both sides by 2:

Plug in 3/2 for x:

Multiply top and bottom by 2:

So one solution is at (3/2 , 5/4).

The other solution happened at y=0:

2y=-x+4

Plug in 0 for y:

2(0)=-x+4

0=-x+4

Add x on both sides:

x=4

So the other point of intersection is (4,0).

-------------------------------------------------------

The two intersections are (3/2 , 5/4) and (4,0).

Now if you don't like that way:

Replace y in bottom equation with (x^2-6x+8):

Distribute:

Subtract 4 on both sides:

Combine like terms:

Compare this to

The quadratic formula is

{Plug in our numbers:

Using 2y+x=4 let's find the correspond y-coordinates.

If x=4:

2y+4=4

Subtract 4 on both sides:

2y=0

Divide both sides by 2:

y=0

So we have (4,0) is a point of intersection.

If x=3/2

2y+(3/2)=4

Subtract (3/2) on both sides:

2y=4-(3/2)

2y=5/2

Divide 2 on both sides:

y=5/4

The other intersection is (3/2 , 5/4).