Which describes the system of equations below? y = 2x + 9/5 y = 2x + 9/5 Choices: (A)consistent and independent (B)inconsistent (C)consistent and dependent

Equations Comparison: We have the system of equations: y = 2x + 9/5 y = 2x + 9/5 First, we need to compare the slopes of both equations. In y = 2x + 9/5, the slope is 2. In y = 2x + 9/5, the slope is also 2. Since both slopes are equal, we can say that the lines are parallel or the same line.Slope and Y-Intercept Analysis: Next, we compare the y-intercepts of both equations. In y = 2x + 9/5, the y-intercept is 9/5. In y = 2x + 9/5, the y-intercept is also 9/5. Since both y-intercepts are equal, we can say that the lines have the same y-intercept.Consistent and Dependent System: Since both the slope and y-intercept of the two equations are the same, the lines represented by these equations are coincident, meaning they lie on top of each other. Therefore, the system of equations has an infinite number of solutions where the two equations intersect, which is everywhere on the line. This means the system of equations is consistent and dependent.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which describes the system of equations below? $\newline$ $y = 2x + \frac{9}{5}$ $\newline$ $y = 2x + \frac{9}{5}$ $\newline$ Choices: $\newline$ (A)consistent and independent $\newline$ (B)inconsistent $\newline$ (C)consistent and dependent

View step-by-step help

Home

Math Problems

Algebra 1

Classify a system of equations

Full solution

Q. Which describes the system of equations below?

\newline

y = 2x + \frac{9}{5}

\newline

y = 2x + \frac{9}{5}

\newline

Choices:

\newline

(A)consistent and independent

\newline

(B)inconsistent

\newline

(C)consistent and dependent

Equations Comparison: We have the system of equations: $\newline$ $y = 2x + \frac{9}{5}$ $\newline$ $y = 2x + \frac{9}{5}$ $\newline$ First, we need to compare the slopes of both equations. $\newline$ In $y = 2x + \frac{9}{5}$ , the slope is $2$ . $\newline$ In $y = 2x + \frac{9}{5}$ , the slope is also $2$ . $\newline$ Since both slopes are equal, we can say that the lines are parallel or the same line.
Slope and Y-Intercept Analysis: Next, we compare the y-intercepts of both equations. In $y = 2x + \frac{9}{5}$ , the y-intercept is $\frac{9}{5}$ . In $y = 2x + \frac{9}{5}$ , the y-intercept is also $\frac{9}{5}$ . Since both y-intercepts are equal, we can say that the lines have the same y-intercept.
Consistent and Dependent System: Since both the slope and $y$ -intercept of the two equations are the same, the lines represented by these equations are coincident, meaning they lie on top of each other. $\newline$ Therefore, the system of equations has an infinite number of solutions where the two equations intersect, which is everywhere on the line. $\newline$ This means the system of equations is consistent and dependent.