Classify each system. Give the number of solutions.

y=3(x-1)
-y+3x=3
My answer :
0=0
Infinitely many(consistent and dependent system)

y-2x=5
X=y-3
My answer:
0=2
No solution(inconsistent system)

Please
My answers are true or false, if my answers are false help me

agree with the first one,

the 2nd is wrong:
y-2x=5, x=y-3
use substitution
y - 2(y-3) = 5
y - 2y + 6 = 5
-y = -1
y = 1, then x = 1-3 = -2
one unique solution.

Let's analyze each system of equations individually to verify your answers:

1. y = 3(x-1)
-y + 3x = 3

To classify this system, we can begin by examining the slopes of the two equations. The first equation, y = 3(x-1), is in slope-intercept form (y = mx + b), where m represents the slope. In this case, we have a slope of 3. The second equation, -y + 3x = 3, can be rearranged to y = 3x - 3, revealing a slope of 3 as well. Since both equations have the same slope, they are considered parallel lines.

Parallel lines do not intersect, meaning they have no common solution. In this case, the system is inconsistent, which aligns with your initial answer of infinitely many solutions. Your answer is correct.

2. y - 2x = 5
x = y - 3

To determine the number of solutions, we will first rewrite the second equation in slope-intercept form. From x = y - 3, we isolate y: y = x + 3. Notice that this equation also has a slope of 1.

Comparing the two equations, y - 2x = 5 and y = x + 3, we can observe that they represent two distinct lines. Since these lines are not parallel and have different slopes, they will intersect at a single point (x, y). Thus, the system has one unique solution.

Your initial answer of 0 = 2, indicating no solution, is incorrect in this case. The system has a single solution. Consequently, your answer is false.

I hope this clarification helps you understand the classification and number of solutions in each system of equations.