How many solutions does the system have? {[y=-3x+9],[3y=-9x+9]:} Choose 1 answer: (A) Exactly one solution (B) No solutions (C) Infinitely many solutions

Analyze First Equation: Let's analyze the first equation: y = -3x + 9 This is a linear equation in slope-intercept form, where the slope is -3 and the y-intercept is 9.Analyze Second Equation: Now let's analyze the second equation: 3y = -9x + 9 To compare it with the first equation, we need to put it in slope-intercept form by dividing every term by 3: y = -3x + 3 This is also a linear equation in slope-intercept form, where the slope is -3 and the y-intercept is 3.Compare Slopes: We compare the slopes of the two equations: Slope of the first equation: -3 Slope of the second equation: -3 The slopes are the same.Compare Y-Intercepts: Next, we compare the y-intercepts of the two equations: y-intercept of the first equation: 9 y-intercept of the second equation: 3 The y-intercepts are different.Final Conclusion: Since the slopes are the same but the y-intercepts are different, the lines are parallel and do not intersect. Therefore, the system of equations has no solutions.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

How many solutions does the system have?

{[y=-3x+9],[3y=-9x+9]:}
Choose 1 answer:
(A) Exactly one solution
(B) No solutions
(C) Infinitely many solutions

How many solutions does the system have? $\newline$ $\left\{\begin{array}{l} y=-3 x+9 \\ 3 y=-9 x+9 \end{array}\right.$ $\newline$ Choose $1$ answer: $\newline$ (A) Exactly one solution $\newline$ (B) No solutions $\newline$ (C) Infinitely many solutions

View step-by-step help

Home

Math Problems

Algebra 2

Find the number of solutions to a system of equations

Full solution

Q. How many solutions does the system have?

\newline

\left\{\begin{array}{l} y=-3 x+9 \\ 3 y=-9 x+9 \end{array}\right.

\newline

Choose

1

answer:

\newline

(A) Exactly one solution

\newline

(B) No solutions

\newline

Analyze First Equation: Let's analyze the first equation: $\newline$ $y = -3x + 9$ $\newline$ This is a linear equation in slope-intercept form, where the slope is $-3$ and the y-intercept is $9$ .
Analyze Second Equation: Now let's analyze the second equation: $\newline$ $3y = -9x + 9$ $\newline$ To compare it with the first equation, we need to put it in slope-intercept form by dividing every term by $3$ : $\newline$ $y = -3x + 3$ $\newline$ This is also a linear equation in slope-intercept form, where the slope is $-3$ and the y-intercept is $3$ .
Compare Slopes: We compare the slopes of the two equations: $\newline$ Slope of the first equation: $-3$ $\newline$ Slope of the second equation: $-3$ $\newline$ The slopes are the same.
Compare Y-Intercepts: Next, we compare the y-intercepts of the two equations: $\newline$ y-intercept of the first equation: $9$ $\newline$ y-intercept of the second equation: $3$ $\newline$ The y-intercepts are different.
Final Conclusion: Since the slopes are the same but the $y$ -intercepts are different, the lines are parallel and do not intersect. $\newline$ Therefore, the system of equations has no solutions.