The system of equations is:
y = 3x - 2
-3x + y = 7
We can solve this system by substitution or elimination method.
Using the elimination method, we can add 3x to both sides of the second equation:
-2x + y = 7
Now, we can see that the first equation and the modified second equation are equivalent.
This means that the system of equations represents the same line.
Since the two equations represent the same line, the system has infinitely many solutions.
Therefore, the answer is ∞.
The graphs represent this system: y=3x−2 −3x+y=7 How many solutions does this system have: 0, 1, or ∞ ? (1 point)
3 answers
Wrong
Apologies for the mistake in my previous response.
To determine the number of solutions, we need to analyze the two equations.
The first equation, y = 3x - 2, represents a straight line with a slope of 3 and a y-intercept of -2.
The second equation, -3x + y = 7, can be rewritten as y = 3x + 7. This equation also represents a straight line with a slope of 3 and a y-intercept of 7.
Since the slopes of both lines are equal, but the y-intercepts are different, these lines are parallel and will never intersect. Therefore, the system of equations has no solution.
The correct answer is 0.
To determine the number of solutions, we need to analyze the two equations.
The first equation, y = 3x - 2, represents a straight line with a slope of 3 and a y-intercept of -2.
The second equation, -3x + y = 7, can be rewritten as y = 3x + 7. This equation also represents a straight line with a slope of 3 and a y-intercept of 7.
Since the slopes of both lines are equal, but the y-intercepts are different, these lines are parallel and will never intersect. Therefore, the system of equations has no solution.
The correct answer is 0.
1 answer