Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

How many solutions does the system of equations below have? $\newline$ $y = \frac{1}{7}x - 2$ $\newline$ $y = \frac{3}{8}x + \frac{1}{2}$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions $\newline$

View step-by-step help

View step-by-step help

Find the number of solutions to a system of equations

Full solution

Q. How many solutions does the system of equations below have?

\newline

y = \frac{1}{7}x - 2

\newline

y = \frac{3}{8}x + \frac{1}{2}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

\newline

Analyze slopes: Analyze the slopes of both equations. The slope of the first equation $y = \frac{1}{7}x - 2$ is $\frac{1}{7}$ . The slope of the second equation $y = \frac{3}{8}x + \frac{1}{2}$ is $\frac{3}{8}$ . Since the slopes are different $\frac{1}{7} \neq \frac{3}{8}$ , the lines are not parallel.
Different slopes: Since the slopes are different, the lines will intersect at exactly one point. This means that there is one unique solution to the system of equations.
Unique solution: There is no need to find the exact point of intersection since we are only asked about the number of solutions. $\newline$ We have determined that there is one solution based on the slopes of the lines.

More problems from Find the number of solutions to a system of equations

Question

Solve using elimination.

\newline

x + 6y = -15

\newline

-2x + 6y = 12

\newline

(\_,\_)

Posted 2 months ago

Question

(1,1)

a solution to this system of equations?

\newline

8x + y = 9

\newline

6x + 12y = 18

\newline

\newline

\newline

Posted 1 month ago

Question

How many solutions does the system of equations below have?

\newline

7

\newline

7

\newline

\newline

\text{[A]no solution}

\newline

\text{[B]one solution}

\newline

\text{[C]infinitely many solutions}

Posted 1 month ago

Question

Which describes the system of equations below?

\newline

y = \frac{1}{7}x - 10

\newline

y = \frac{1}{7}x - 10

\newline

\newline

\text{[A]consistent and independent}

\newline

\text{[B]consistent and dependent}

\newline

\text{[C]inconsistent}

Posted 1 month ago

Question

Solve using substitution.

\newline

y = -5

\newline

-4x + 3y = 17

\newline

Posted 1 month ago

Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

\newline

Last Wednesday, two friends met up after school to read the book they were both assigned in Literature class. Bryan can read

2

pages per minute, and he had already read

98

pages. Jayla, who has a reading speed of

3

pages per minute, had read

48

pages. Eventually they had read the same number of pages. How long did that take? How many pages had each of them read?

\newline

\_\_\_\_

minutes, Bryan and Jayla had each read

\_\_\_\_

Posted 1 month ago

Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

At the Castroville Ice Cream Parlor, one group of friends ordered

1

small serving of ice cream and

3

large servings of ice cream for

20

. Another group of friends ordered

1

small serving of ice cream and

4

large servings of ice cream for

26

. How much does the ice cream cost?

\newline

The ice cream costs `\$`_____ for a small serving and `\$`_____ for a large serving.

Posted 1 month ago

Question

\newline

y = -1

\newline

-2x - 4y = 8

\newline

(_____ , _____)

Posted 1 month ago

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

\newline

There are two mystery numbers. The sum of

3

times the first number and

3

times the second number is

-18

2

times the first number and

3

times the second number is

-13

. What are the two numbers?

\newline

The first number is ______ , and the second number is ______.

Posted 1 month ago

Question

A teacher purchased

300

colored pencils for an upcoming project. The pencils she ordered come in packs of

20

30

14

packs in all. Write a system of equations to find the number of

20

(x)

30

(y)

the art teacher ordered.

Posted 2 months ago