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sheccidmariscal9428
18.07.2019 •
Mathematics
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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Ответ:
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![ax^2+bx+c=0](/tpl/images/0103/6339/2bf73.png)
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).
Ответ:
Take the log of each side, any base will work
so log4, loge or log10
Step-by-step explanation:
4^ (x+3) = 18
Take the log of each side
loga (4^ (x+3)) = loga 18
We can the take the exponents outside of the log
(x+3) loga 4 = loga 18
Divide each side by loga 4
(x+3) = loga 18 /loga 4
Subtract 3 from each side
x = loga 18 /loga 4 -3