Mathematics, 18.07.2019 10:10 jaz5380

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

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Answer from: gransazer863

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:

y=x^2-6x+8

2y+x=4 .

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:

y=(x-4)(x-2)

-2y=x-4

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

y=-2y(x-2)

So one solution will occur when y is 0.

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

1=-2(x-2)

Distribute:

1=-2x+4

Subtract 4 on both sides:

-3=-2x

Divide both sides by -2:

$\frac{-3}{-2}=x$

$\frac{3}{2}=x$

$x=\frac{3}{2}$

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

2y=-x+4

Divide both sides by 2:

$y=\frac{-x+4}{2}$

Plug in 3/2 for x:

$y=\frac{\frac{-3}{2}+4}{2}$

Multiply top and bottom by 2:

$y=\frac{-3+8}{4}$

$y=\frac{5}{4}$

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:

y=x^2-6x+8

2y+x=4

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

2(x^2-6x+8)+x=4

Distribute:

2x^2-12x+16+x=4

Subtract 4 on both sides:

2x^2-12x+16+x-4=0

Combine like terms:

2x^2-11x+12=0

Compare this to ax^2+bx+c=0

a=2

b=-11

c=12

The quadratic formula is

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

{Plug in our numbers:

$x=\frac{11 \pm \sqrt{(-11)^2-4(2)(12)}}{2(2)}$

$x=\frac{11 \pm \sqrt{121-96}}{4}$

$x=\frac{11 \pm \sqrt{25}}{4}$

$x=\frac{11 \pm 5}{4}$

$x=\frac{11+5}{4} \text{ or } \frac{11-5}{4}$

$x=\frac{16}{4} \text{ or } \frac{6}{4}$

$x=4 \text{ or } \frac{3}{2}$

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).

Answer from: Quest

left 3, up 4

step-by-step explanation:

just count the values of x & y of the vertex of the graph and see how many units in the x and y direction will get you from the f(x) graph to the f(x) graph

Which best describes the transformation that occurs from the graph of f(x) = x to g(x) = (x + 3)2 +

Answer from: Quest

i dont know sorry

step-by-step explanation:

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Y= x2 − 6x + 8
2y + x = 4
the pair of points representing the solution set of this syst...

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