Ask question

Ask question

All categories

3 years ago

13

Classify the system as independent, dependent, or inconsistent.

1 answer:

Anastasy [175]3 years ago

7 0

1. 4x + 8y = 12....divide by 4
x + 2y = 3
2y = -x + 3
y = -1/2x + 3/2...slope is -1/2, y int is 3/2

x + 2y = -3
2y = -x - 3
y = -1/2x - 3/2...slope is -1/2 and y int is -3/2

when the slopes are the same, and the y int are different, then the lines are parallel and never intersect...so they have no solution and are inconsistent
=================
2. y = 2x - 1...slope is 2 and y int is -1
y = -2x + 5 ...slope is -2 and y int is 5
when the slopes are different and the y int are different, then there is 1 solution making it independent
=================
3. 4x - 12y = 8...divide by 4
x - 3y = 2
same as other equation meaning the equations are the same line...meaning they have infinite solutions making them dependent

You might be interested in

If 5 + 20 times 2 Superscript 2 minus 3 x Baseline = 10 times 2 Superscript negative 2 x Baseline + 5, what is the value of x? –

sp2606 [1]

Answer:

<h3>Option D) 3 is correct</h3><h3>Therefore the value of x is 3</h3>

Step-by-step explanation:

Given equation is $5+20\times (2)^{2-3x}=10\times (2)^{-2x}+5$

<h3>To find the value of x :</h3>

First solving the given equation we have,

$5+20\times (2)^{2-3x}=10\times (2)^{-2x}+5$

$5+20\times (2)^{2-3x}-5=10\times (2)^{-2x}+5-5$

$20\times (2)^{2-3x}=10\times (2)^{-2x}$

$20\times (2)^2.(2)^{-3x}=10\times (2)^{-2x}$

$20\times 4.(2)^{-3x}=10\times (2)^{-2x}$

$80(2)^{-3x}=10\times (2)^{-2x}$

$\frac{80}{10}(2)^{-3x}=\frac{10\times (2)^{-2x}}{10}$

$8(2)^{-3x}=(2)^{-2x}$

$\frac{(2)^{-3x}}{(2)^{-2x}}=\frac{1}{8}$

$(2)^{-3x}.(2)^{2x}=\frac{1}{2^3}$ ( by using the property $\frac{1}{a^{-m}}=a^m$ )

$2^{-3x+2x}=\frac{1}{2^3}$ ( by using the property $a^m.a^n=a^{m+n}$ )

$2^{-x}=\frac{1}{2^3}$

$\frac{1}{2^x}=\frac{1}{2^3}$ ( by using the property $a^{-m}=\frac{1}{a^m}$ )

Since bases are same so powers are same

Therefore we can equate the powers we get x=3

<h3>Therefore the value of x is 3</h3><h3>Option D) 3 is correct</h3>

5 0

3 years ago

Read 2 more answers

Sorry it’s so large u can zoom in

nataly862011 [7]

Answer:

15 feet

Step-by-step explanation:

dyscshdududhsgs. don't mind that

6 0

3 years ago

A man is filling an empty 5 gallon bucket with water at a constant rate there are 2.4 gallons of water in the bucket after filli

Fiesta28 [93]

2.4g / 12 minutes

0.2g/minutes

Answer is 0.2 gallons per minute

4 0

3 years ago

brilliants [131]

Answer:

y = 1

Step-by-step explanation:

x + y = 16

x - y = 14 add the equations

--------------

2x = 30

x = 15

x + y = 16

15 + y = 16

y = 1

the numbers are 15 and 1

7 0

3 years ago

You have 35 yards of ribbon for your gift boxes. Each box gets the same amount of ribbon. How much ribbon will each of your 30 g

Lubov Fominskaja [6]

1.16 of a yard, don’t know if this is correct but worth a shot

6 0

2 years ago

Read 2 more answers