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Tamiku [17]
3 years ago
11

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 2x-y=

5 and 4x+ky=2
Mathematics
1 answer:
Bond [772]3 years ago
8 0

Answer:

The system of linear equations has infinitely many solutions

Step-by-step explanation:

Let's modified the equations and find the answer.

Using the first equation:

2x-y=5 we can multiply by 2 in both sides, obtaining:

2*(2x-y)=2*5 which can by simplified as:

4x-2y=10 which is equal to:

4x=2y+10

Considering the second equation:

=4x+ky=2

Taking into account that from the first equation we know that: 4x=2y+10, we can express the second equation as:

2y+10+ky=2, which can be simplified as:

(2+k)y=2-10

(2+k)y=-8

y=-8/(2+k)

Because (-8) is being divided by (2+k), then (2+k) can't be equal to 0, so:

2+k=0 if k=-2

This means that k can be any number different than -2, and for each of these solutions, there is a different solution for y, allowing also, different solutions for x.

For example, if k=0 then

y=-8/(2+0) which give us y=-4, and, because:

4x=2y+10 if y=-4 then x=(-8+10)/4=0.5

Now let's try with k=-1, then:

y=-8/(2-1) which give us y=-8, and, because:

4x=2y+10 if y=-8 then x=(-16+10)/4=-1.5.

Then, the system of linear equations has infinitely many solutions

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Please help! Thanks
9966 [12]

Answer:

x = +-sqrt(3) and they are the actual solutions

Step-by-step explanation:

x^2/ (2x-6) = 9/(6x-18)

get a common denominator of 6x-18

x^2/ (2x-6) * 3/3 = 9/(6x-18)

3x^2/ (6x-18) = 9/(6x-18)

since the denominators are the same, the numerators must be the same

3x^2 = 9

divide by 3 on each side

x^2 = 3

take the square root of each side

sqrt(x^2) = +-sqrt(3)

x = +-sqrt(3)



5 0
3 years ago
The sum of two numbers is 56. Their product is 108. Find the larger number?
lakkis [162]

Answer:

Step-by-step explanation:

The two numbers are 54 and 2

Their sum = 54 + 2 = 56

Their product = 54 x 2 = 108

4 0
3 years ago
Read 2 more answers
If the product of two positive numbers is forty eight, and one number is two greater than the other, what are the two numbers?
zaharov [31]
The two numbers are eight and six
3 0
3 years ago
How many of each angles are in a pentagon
Illusion [34]

There are 108 degrees in each interior angle of a regular pentagon .


I hope that's help !

8 0
3 years ago
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LA = 5x -5<br> B = 3 + 13<br> B<br> Solve for r and then find the measure of B:
topjm [15]

Answer:

x = 9º

∠B = 40º

Step-by-step explanation:

5x-5º = 3x+13º

<em>[add 5 to both sides]</em>

5x = 3x+18º

<em>[subtract 3x from both sides]</em>

2x = 18º

<em>[divide each side by 2]</em>

x = 9º

/ / / / / / / / / / / / / / / / / / /

3x+13º = 3(9º)+13º=27º+13º = 40º

6 0
3 years ago
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