43/21 decimal rounded to the nearest hundredth

Give a geometric description of the following system of equations.a. 2x−4y=12 −3x+6y=−15.b. 2x−4y=12 −5x+3y=10.a. 2x−4y=12 −3x+6

Reptile [31]

Answer:

a. No solution, parallel lines.

b. One solution.

Step-by-step explanation:

Given the system of equations:

a. $2x-4y=12$

$-3x+6y=-15$

b. $2x-4y=12$

$-5x+3y=10$

To give a geometric description of the given system of equations.

The geometric description of a system of equations in 2 variables mean the system of equations will represent the number of lines equal to the number of equations in the system given.

i.e.

Number of planes = Number of variables

Number of lines = Number of equations in the system.

Here, we are given 2 variables and 2 equation in each system.

So, they can be represented in the xy-coordinates plane.

And the number of solutions to the system depends on the following condition.

Let the system of equations be:

$A_1x+B_1y+C_1=0\\A_2x+B_2y+C_2=0$

1. One solution:

There will be one solution to the system of equations, If we have:

$\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}$

2. Infinitely Many Solutions: (Identical lines in the system)

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}= \dfrac{C_1}{C_2}$

3. No Solution:(Parallel lines)

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}\neq\dfrac{C_1}{C_2}$

Now, let us discuss the system of equations one by one:

a. $2x-4y=12$ OR $2x-4y-12=0$

$-3x+6y=-15$ OR $-3x+6y+15=0$

$A_1 = 2, B_1 = -4, C_1 = -12\\A_2 = -3, B_2 = 6, C_2= 15$

Here, the ratio:

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2} = -\dfrac{2}{3}\\\dfrac{C_1}{C_2} = -\dfrac{4}{5}$

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}\neq\dfrac{C_1}{C_2}$

Therefore, no solution i.e. parallel lines.

b. $2x-4y=12$ OR $2x-4y-12=0$

$-5x+3y=10$ OR $-5x+3y-10=0$

$A_1 = 2, B_1 = -4, C_1 = -12\\A_2 = -5, B_2 = 3, C_2 = -10$

$\dfrac{A_1}{A_2}= -\dfrac{2}{5}\\\dfrac{B_1}{B_2} = -\dfrac{4}{3}\\\dfrac{C_1}{C_2} = -\dfrac{6}{5}$

$\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}$

So, one solution.

Kindly refer to the images attached for the graphical representation of the given system of equations.

6 0

2 years ago

Find -1 2/3 + 5/6 on the number line

chubhunter [2.5K]

The answer would be be between 1 and 0.7

7 0

3 years ago

Help pls and thank uu

Sergio039 [100]

Answer:

f(- 4) = - 4

Step-by-step explanation:

f(- 4) with x = - 4 gives f(- 4) = - 4

5 0

3 years ago

The areas of two similar triangles are 9cm2, and 49cm2. One of the sides of the first triangle is 2cm. What is the length of the

BlackZzzverrR [31]

Answer:

4 2/3 cm

Step-by-step explanation:

When we have area, it is the related to the scale factor by the scale factor squared

Area large/ area of small = 49/9

Take the square root

sqrt(49/9) = 7/3

The scale factor is 7/3 large to small

The small side is 2 cm

large 7 x cm

-------- = ------ = -----------

small 3 2 cm

Using cross products

7*2 = 3x

Divide by 3

14/3 = 3x/3

14/3 = the large side

4 2/3 cm

3 0

2 years ago

What is a-5/6= -3 2/3 + 5/6

valentinak56 [21]

Answer:

A=-2

Step-by-step explanation:

iekdkdkdkdkdkdkdkdkkdd

3 0

3 years ago