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How many solutions does the system of equations below have? $\newline$ $y = -2x - 1$ $\newline$ $y = \frac{9}{7}x + \frac{3}{5}$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions

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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 = -2x - 1

\newline

y = \frac{9}{7}x + \frac{3}{5}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Analyze slopes of equations: Analyze the slopes of the given equations. $\newline$ The slope of the first equation $y = -2x - 1$ is $-2$ . $\newline$ The slope of the second equation $y = \frac{9}{7}x + \frac{3}{5}$ is $\frac{9}{7}$ . $\newline$ Since the slopes are different, the lines are not parallel.
Determine if lines intersect: Determine if the lines intersect. $\newline$ Since the slopes are different, the lines must intersect at exactly one point. $\newline$ Therefore, the system of equations has one solution.

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

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(\_,\_)

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(1,1)

a solution to this system of equations?

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6x + 12y = 18

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\newline

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Question

How many solutions does the system of equations below have?

\newline

7

\newline

7

\newline

\newline

\text{[A]no solution}

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\text{[B]one solution}

\newline

\text{[C]infinitely many solutions}

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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}

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\text{[C]inconsistent}

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Question

Solve using substitution.

\newline

y = -5

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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

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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

\_\_\_\_

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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

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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

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. How much does the ice cream cost?

\newline

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

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Question

\newline

y = -1

\newline

-2x - 4y = 8

\newline

(_____ , _____)

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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

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times the first number and

3

times the second number is

-18

2

times the first number and

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times the second number is

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. What are the two numbers?

\newline

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

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Question

A teacher purchased

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

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30

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

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(x)

30

(y)

the art teacher ordered.

Posted 8 months ago

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