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? $\newline$ $y = \frac{3}{10}x + \frac{5}{9}$ $\newline$ $y = -\frac{3}{10}x + \frac{5}{9}$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions

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{3}{10}x + \frac{5}{9}

\newline

y = -\frac{3}{10}x + \frac{5}{9}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Slope Comparison: System of equations: $\newline$ $y = \frac{3}{10}x + \frac{5}{9}$ $\newline$ $y = -\frac{3}{10}x + \frac{5}{9}$ $\newline$ Are the slopes same or different? $\newline$ Slope of first equation: $\frac{3}{10}$ $\newline$ Slope of second equation: $-\frac{3}{10}$ $\newline$ Slopes of the equations are different.
Y-Intercept Comparison: System of equations: $\newline$ $y = \frac{3}{10}x + \frac{5}{9}$ $\newline$ $y = -\frac{3}{10}x + \frac{5}{9}$ $\newline$ Are the y-intercepts same or different? $\newline$ y-intercept of first equation: $\frac{5}{9}$ $\newline$ y-intercept of second equation: $\frac{5}{9}$ $\newline$ y-intercepts of the equations are the same.
Number of Solutions: System of equations: $\newline$ $y = \frac{3}{10}x + \frac{5}{9}$ $\newline$ $y = -\frac{3}{10}x + \frac{5}{9}$ $\newline$ Determine the number of solutions to the system of equations. $\newline$ The system of equations has different slopes and the same $y$ -intercept. $\newline$ The system of equations has $1$ solution, where the two lines intersect.

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