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How many solutions does the system of equations below have? $\newline$ $y = -6x + 8$ $\newline$ $y = -6x - \frac{3}{7}$ $\newline$ 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 = -6x + 8

\newline

y = -6x - \frac{3}{7}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Slope Analysis: System of equations: $\newline$ $y = -6x + 8$ $\newline$ $y = -6x - \frac{3}{7}$ $\newline$ Are the slopes same or different? $\newline$ Slope of first equation: $-6$ $\newline$ Slope of second equation: $-6$ $\newline$ Slopes of the equations are the same.
Y-Intercept Comparison: System of equations: $\newline$ $y = -6x + 8$ $\newline$ $y = -6x - \frac{3}{7}$ $\newline$ Are the y-intercepts same or different? $\newline$ y-intercept of first equation: $8$ $\newline$ y-intercept of second equation: $-\frac{3}{7}$ $\newline$ y-intercepts of the equations are different.
Number of Solutions: System of equations: $\newline$ $y = -6x + 8$ $\newline$ $y = -6x - \frac{3}{7}$ $\newline$ 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

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How many solutions does the system of equations below have?

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7

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7

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\text{[A]no solution}

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Which describes the system of equations below?

\newline

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\newline

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

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\newline

\text{[A]consistent and independent}

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\text{[B]consistent and dependent}

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\newline

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

\newline

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pages. Jayla, who has a reading speed of

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pages per minute, had read

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\newline

\_\_\_\_

minutes, Bryan and Jayla had each read

\_\_\_\_

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

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

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\newline

y = -1

\newline

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\newline

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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

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times the first number and

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Question

A teacher purchased

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30

(y)

the art teacher ordered.

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