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Shtirlitz [24]
3 years ago
15

6x−3y=5 y−2x=8 ​ How many solutions does the system have?

Mathematics
2 answers:
dybincka [34]3 years ago
7 0

Answer:

no solution.

Step-by-step explanation:

We have been given the system of equations

6x-3y=5...(i)

y-2x=8...(ii)

Write both equations in slope intercept form y = mx +b

For equation (i)

6x-3y=5\\-3y=-6x+5\\\\y=2x-\frac{5}{3}

The slope is 2 and the y- intercept is -5/3

For equation (ii)

y-2x=8\\\\y=2x+8

The slope is 2 and the y-intercept is 8

Since, both the equations have equal slope and different y - intercepts. Hence, the lines are parallel.

Therefore, we can say that the system have no solution.

zhuklara [117]3 years ago
3 0

No Solutions because there are too many = signs.

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7 0
3 years ago
Discrete Math
andrezito [222]

Answer:

Part c: Contained within the explanation

Part b: gcd(1200,560)=80

Part a: q=-6         r=1

Step-by-step explanation:

I will start with c and work my way up:

Part c:

Proof:

We want to shoe that bL=a+c for some integer L given:

bM=a for some integer M and bK=c for some integer K.

If a=bM and c=bK,

then a+c=bM+bK.

a+c=bM+bK

a+c=b(M+K) by factoring using distributive property

Now we have what we wanted to prove since integers are closed under addition.  M+K is an integer since M and K are integers.

So L=M+K in bL=a+c.

We have shown b|(a+c) given b|a and b|c.

//

Part b:

We are going to use Euclidean's Algorithm.

Start with bigger number and see how much smaller number goes into it:

1200=2(560)+80

560=80(7)

This implies the remainder before the remainder is 0 is the greatest common factor of 1200 and 560. So the greatest common factor of 1200 and 560 is 80.

Part a:

Find q and r such that:

-65=q(11)+r

We want to find q and r such that they satisfy the division algorithm.

r is suppose to be a positive integer less than 11.

So q=-6 gives:

-65=(-6)(11)+r

-65=-66+r

So r=1 since r=-65+66.

So q=-6 while r=1.

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Given f(x) = 7x^9, find f^-1 (x). Then state whether f^-1 (x) is a function
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A though without graphing software it would appear to be C


Step-by-step explanation:
The inverse of a function is the function reflected across the line y=x. This results in the coordinate points (x,y) of the function becoming (y,x) for the inverse function. Algebraically to find the inverse, switch the x and y locations and solve for y.
y = 7x^9
x = 7y^9
x/7 = y^9
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This is a ninth root of (x/7) also written in exponents as y = (x/7)^(1/9).
This is a function. While it appears not to be a function because the middle portion over the origin appears vertical, it is a function because the middle portion over the origin is changing and graphing software shows it has no input with more than one output. Without graphing software you would rule it is not a function.
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