How many solutions does the system of equations below have? y = 10/7x + 4 y = 10/7x − 2/7 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Analyze Equations: Step 1: Analyze the equations. y = 10/7x + 4 y = 10/7x - 2/7 Both equations have the same slope (10/7), which means they are parallel lines unless they are the same line. Check Y-Intercepts: Step 2: Check if the y-intercepts are the same. The first equation has a y-intercept of 4, and the second has a y-intercept of -2/7. Since 4 ≠ -2/7, the lines are not the same. Determine Solutions: Step 3: Determine the number of solutions. Parallel lines that are not identical do not intersect. Therefore, there are no points where both equations are true simultaneously.

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How many solutions does the system of equations below have? $\newline$ $y = \frac{10}{7}x + 4$ $\newline$ $y = \frac{10}{7}x - \frac{2}{7}$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions

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Math Problems

Grade 8

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 = \frac{10}{7}x + 4

\newline

y = \frac{10}{7}x - \frac{2}{7}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Analyze Equations: Step $1$ : Analyze the equations. $\newline$ $y = \frac{10}{7}x + 4$ $\newline$ $y = \frac{10}{7}x - \frac{2}{7}$ $\newline$ Both equations have the same slope ( $\frac{10}{7}$ ), which means they are parallel lines unless they are the same line.
Check Y-Intercepts: Step $2$ : Check if the y-intercepts are the same. $\newline$ The first equation has a y-intercept of $4$ , and the second has a y-intercept of $-\frac{2}{7}$ . Since $4 \neq -\frac{2}{7}$ , the lines are not the same.
Determine Solutions: Step $3$ : Determine the number of solutions. Parallel lines that are not identical do not intersect. Therefore, there are no points where both equations are true simultaneously.