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

Divide Second Equation: We have the system of equations: y = -3x + 9 3y = -9x + 9 Let's first simplify the second equation by dividing each term by 3 to make it easier to compare with the first equation.Compare Slopes: After dividing the second equation by 3, we get: y = -3x + 3 Now we have two equations: y = -3x + 9 y = -3x + 3 Let's compare the slopes of these two equations.Compare Y-Intercepts: Slope of the first equation: -3 Slope of the second equation: -3 The slopes of both equations are the same.Determine Intersection: Next, let's 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.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.

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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

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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

Divide Second Equation: We have the system of equations: $\newline$ $y = -3x + 9$ $\newline$ $3y = -9x + 27$ $\newline$ Let's first simplify the second equation by dividing each term by $3$ to make it easier to compare with the first equation.
Compare Slopes: After dividing the second equation by $3$ , we get: $\newline$ $y = -3x + 3$ $\newline$ Now we have two equations: $\newline$ $y = -3x + 9$ $\newline$ $y = -3x + 3$ $\newline$ Let's compare the slopes of these two equations.
Compare Y-Intercepts: Slope of the first equation: $-3$ Slope of the second equation: $-3$ The slopes of both equations are the same.
Determine Intersection: Next, let's 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.
Determine Intersection: Next, let's 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.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.