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3 years ago

Solve the system of equations: y = 2x + 1 y = x2 + 2x - 8

Mathematics

1 answer:

Elan Coil [88]3 years ago

4 0

(3,7),(-3,-5)

that’s what it would look like on a graph

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Which system of equations has only one solution? 4 x + 2 y = 8. Negative 4 x minus 2 y = 3. Negative 5 x + y = 6. 5 x minus y =

madam [21]

Answer:

Following system of equations have exactly one solution:

$2 x + 4 y = 6\\ 3 x - 4 y = 9$

Step-by-step explanation:

Given 4 system of equations:

1st

$4 x + 2 y = 8\\ -4 x -2 y = 3$

2nd

$-5 x + y = 6\\ 5 x - y = - 6$

3rd

$- 3 x + 4 y = 2\\ 3 x - 4 y = 0$

4th

$2 x + 4 y = 6\\ 3 x - 4 y = 9$

To find: Which system of equations has only one solution?

Solution:

First of all, let us learn the concept.

Let the equation of lines be:

$a_1x+b_1y+ c_1=0$ and $a_2x+b_2y+ c_2=0$

1. No solution:

There exists no solution if:

$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}$

2. Infinite solutions:

There exist infinitely many solutions if:

$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}$

3. One solution:

There exists one solution if:

$\dfrac{a_1}{a_2}\neq\dfrac{b_1}{b_2}$

Now, let us consider the given equations one by one.

1st system of equations:

The ratio is:

$\dfrac{4}{-4} , \dfrac{2}{-2} , \dfrac{8}{3}\\-1 =-1\neq \dfrac{8}{3}$

So, no solution.

2nd system of equations:

The ratio:

$\dfrac{-5}{5} , \dfrac{-1}{1} , \dfrac{6}{-6}\\-1 =-1=-1$

So, infinitely many solutions.

3rd system of equations:

$\dfrac{3}{-3} , \dfrac{-4}{4} , \dfrac{0}{2}\\-1 =-1\ne0$

So, no solution.

4th system of equations:

$\dfrac{2}{3} , \dfrac{4}{-4} , \dfrac{6}{9}\\\dfrac{2}{3} \ne-1$

Hence, only one solution.

So, the answer is:

Following system of equations have only one solution:

$2 x + 4 y = 6\\ 3 x - 4 y = 9$

8 0

4 years ago

I’m not sure what this means

Orlov [11]

These are independent so probability of one does not affect the other.
1. P = 1/8 * 1/6 = 1/48
2. P=1/8 * 3/6 = 3/48 or 1/16
3. P= 4/8 * 1/6 = 4/48 or 1/12
4. P= 4/8 * 3/6 = 12/48 or 1/4
5. P= 5/8 * 2/6 = 10/48 or 5/24
6. P= 4/8 * 2/6 = 8/48 or 1/6

5 0

2 years ago