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How many solutions does the system of equations below have? $\newline$ $y = -2x + \frac{9}{7}$ $\newline$ $y = -2x + \frac{7}{9}$ $\newline$ 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

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

\newline

y = -2x + \frac{9}{7}

\newline

y = -2x + \frac{7}{9}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Slope Analysis: System of equations: $\newline$ $y = -2x + \frac{9}{7}$ $\newline$ $y = -2x + \frac{7}{9}$ $\newline$ Are the slopes same or different? $\newline$ Slope of first equation: $-2$ $\newline$ Slope of second equation: $-2$ $\newline$ Slopes of the equations are the same.
Y-Intercept Comparison: System of equations: $\newline$ $y = -2x + \frac{9}{7}$ $\newline$ $y = -2x + \frac{7}{9}$ $\newline$ Are the y-intercepts same or different? $\newline$ y-intercept of first equation: $\frac{9}{7}$ $\newline$ y-intercept of second equation: $\frac{7}{9}$ $\newline$ y-intercepts of the equations are different.
Number of Solutions: System of equations: $\newline$ $y = -2x + \frac{9}{7}$ $\newline$ $y = -2x + \frac{7}{9}$ $\newline$ Determine the number of solutions to the system of equations. $\newline$ The system of equations has the same slope but different $y$ -intercepts. $\newline$ The system of equations has no solution because they are parallel lines that never intersect.

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

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Solve using elimination.

\newline

x + 6y = -15

\newline

-2x + 6y = 12

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(1,1)

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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}

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\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}

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\text{[B]consistent and dependent}

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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

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

\_\_\_\_

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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

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. 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?

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

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\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

300

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.

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