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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

Mrs. Magdalino kept records on how much she spent on gasoline and the maintenance of her car. She found that it cost $485 to dri

algol [13]

Answer:

C = 0.97m
$1164 for 1200 miles
845 miles for $820

Step-by-step explanation:

Given a car's cost of operation is $485 for 500 miles, you want an equation relating cost for m miles, and solutions to that equation for 1200 miles, and for a cost of $820.

The cost per mile is found by dividing the cost by the associated number of miles:

$485/(500 mi) = $0.97 /mi

<h3>Equation</h3>

The equation for the cost will show the cost as the cost per mile multiplied by the number of miles:

C = 0.97m . . . . . where C is cost in dollars for m miles driven

<h3>1200 miles</h3>

The cost for driving $1200 miles will be ...

C = 0.97(1200) = $1164

The cost of driving 1200 miles is $1164.

The number of miles that can be driven for a cost of $820 is ...

820 = 0.97m

m = 820/0.97 = 845.36

About 845 miles are driven for a cost of $820.

3 0

10 months ago

A deck is in the shape of a square. The area of the deck is 576 swuare feet. which is the length of each side of the deck

NNADVOKAT [17]

A) 24

All side lengths of a square are equal so you take the square root of 576 to get two 24. If you try it back: 24*24 (w*h) to get 576.

7 0

2 years ago

Read 2 more answers

Match each shape on the left with its area formula on the right.

e-lub [12.9K]

Step-by-step explanation:

A=1/2(B1+B2)h is a trapezoid

A=1/2bh is a triangle

A=bh is a parallelogram

And A=Pir2 is a circle

5 0

3 years ago

Please answer :puppy eyes emoji:

Anettt [7]

Well ven diagrams help you visually compare and contrast two figures. They helps you note the similarities and the differences between two items. Hope this helps!

8 0

2 years ago