1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
zhannawk [14.2K]
3 years ago
6

How are slopes and y intercepts to the number of solutions of a system of the liner

Mathematics
1 answer:
Leona [35]3 years ago
7 0
We assume a linear system with 2 variables.


If the slopes are the same, and y-intercepts are different, there are 0 solutions.

If the slopes are different, there is 1 solution.

If the slopes are the same, and the y-intercepts are the same, there are ∞ solutions.
You might be interested in
Don’t really know what linear functions are
kondaur [170]

Answer:

The rate of change of f(x) is greater than that of g(x)

They have the same y intercept of 14

Step-by-step explanation:

Given

g(x) = -\frac{1}{2}x + 14

Table for function f(x)

Required

Compare their rate of change and intercept

For g(x), we have:

g(x) = -\frac{1}{2}x + 14

The form of an equation is:

y = mx + b

Where

m = slope

b =y\ intercept

So:

m = -\frac{1}{4}

b = 14

For f(x): Start by calculating the slope (m)

m = \frac{y_2 - y_1}{x_2 - x_1}

m = \frac{17-16}{6-4}

m = \frac{1}{2}

The intercept is calculated using:

m = \frac{y_2 - y_1}{x_2 - x_1}

Where

(x_1,y_1) = (-2,13)

(x_2,y_2) = (0,y) --- we want to solve for y

So:

\frac{1}{2} = \frac{y - 13}{0 --2}

\frac{1}{2} = \frac{y - 13}{2}

Multiply both sides by 2

1 =y - 13

Make y the subject

y =1 + 13

y = 14

So, we have:

m = -\frac{1}{4} and b = 14 -- for g(x)

m = \frac{1}{2} and y = 14 --- for f(x)

By comparison:

The rate of change (i.e. slope) of f(x) is greater than that of g(x) because 1/2 > -1/2

They have the same y intercept of 14

3 0
3 years ago
List the first 5 multiples of, find all the factors of 7
Aleksandr [31]
What # do you need the first five multiples for? and the only factors for 7 are one and seven because it is a prime number!
8 0
3 years ago
Read 2 more answers
Consider the matrix shown below:
WINSTONCH [101]

Answer:

A

Step-by-step explanation:

P^T is transpote matrix. So the rows of matrix P you write like columns in P^T.

So we have first row: 2, 5, it will be firsl column

2nd row: 8,1 will be 2nd column.

It is matrix:

2 8

5 1

This is matrix a)

3 0
3 years ago
12 divided by 1 1/5 = ? <br><br> IN lowest TERM
kompoz [17]

Answer:

12 divided by 1 1/5 = 60/11 in lowest term

I hope this helps you.

Step-by-step explanation:

Simplify the expression.

5 0
3 years ago
Nicole has a collection of dolls that weigh 2/2 gram. How much would 2 dolls weigh?
SashulF [63]

Answer:

2

Step-by-step explanation:

Because 2/2 equals 1, and 1 * 2 = 2

7 0
3 years ago
Other questions:
  • What is the value of x?<br> Enter your answer in the box.<br><br> x = ________
    9·1 answer
  • Pleas help me !!!!!!!!
    15·2 answers
  • For which value of c is the line y=3x+c a tangent to the parabola with equation y=x^2-5x+7
    5·1 answer
  • I need help with this equation. -2x = 10
    5·2 answers
  • Evaluate the function. Find f(5). f(x)=2x2-1. The second 2 is a exponent
    8·1 answer
  • Solve for x. <br><br> −2 = 3/9x
    10·1 answer
  • A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25
    6·1 answer
  • Slope and y intercept of 6x=4y-8 with work shown please
    6·2 answers
  • Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.
    10·2 answers
  • If f(x) = 2x^2 +1 and g(x) = 3x-2 what is the value of f(g(x))
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!