The point (2,5) is a solution to which system of equations?
A. y=x-8
2x+y=7
B. y = -1/2x+6
y=3x-1
C. y = x + 2
y = x + 5
D. y = 2/3x +6
3y + 6x - 18 =0
To determine which system of equations the point (2,5) is a solution to, we can substitute the values of x and y into each equation in the given systems and see if both equations are satisfied.
A. y=x-8
Substituting x=2 and y=5:
5 = 2 - 8
5 = -6
This equation is not satisfied by the point (2,5).
2x+y = 7
Substituting x=2 and y=5:
2(2) + 5 = 7
4 + 5 = 7
9 = 7
This equation is also not satisfied by the point (2,5).
Therefore, the point (2,5) is not a solution to system A.
B. y = -1/2x+6
Substituting x=2 and y=5:
5 = -(1/2)(2) + 6
5 = -1 + 6
5 = 5
This equation is satisfied by the point (2,5).
y=3x-1
Substituting x=2 and y=5:
5 = 3(2) - 1
5 = 6 - 1
5 = 5
This equation is also satisfied by the point (2,5).
Therefore, the point (2,5) is a solution to system B.
Similarly, we can test the remaining options.
C. y = x + 2
Substituting x=2 and y=5:
5 = 2 + 2
5 = 4
This equation is not satisfied by the point (2,5).
y = x + 5
Substituting x=2 and y=5:
5 = 2 + 5
5 = 7
This equation is also not satisfied by the point (2,5).
Therefore, the point (2,5) is not a solution to system C.
D. y = 2/3x + 6
Substituting x=2 and y=5:
5 = (2/3)(2) + 6
5 = 4/3 + 6
5 = 22/3
This equation is not satisfied by the point (2,5).
3y + 6x - 18 = 0
Substituting x=2 and y=5:
3(5) + 6(2) - 18 = 0
15 + 12 - 18 = 0
15 + 12 - 18 = -6
This equation is also not satisfied by the point (2,5).
Therefore, the point (2,5) is not a solution to system D.
In conclusion, the point (2,5) is a solution to system B, which consists of the equations:
y = -1/2x+6
y = 3x-1
To determine which system of equations the point (2,5) is a solution to, we need to substitute the values of x and y into both equations and check if they are satisfied.
Let's go through the options one by one:
A. y = x - 8
2x + y = 7
Substituting x = 2 and y = 5 into the equations:
5 = 2 - 8 (Not satisfied)
2(2) + 5 = 7 (Satisfied)
Since the first equation is not satisfied, the point (2,5) is not a solution to this system.
B. y = -1/2x + 6
y = 3x - 1
Substituting x = 2 and y = 5 into the equations:
5 = -1/2(2) + 6 (Satisfied)
5 = 3(2) - 1 (Satisfied)
The point (2,5) is a solution to this system.
C. y = x + 2
y = x + 5
Substituting x = 2 and y = 5 into the equations:
5 = 2 + 2 (Not satisfied)
5 = 2 + 5 (Not satisfied)
The point (2,5) is not a solution to this system.
D. y = 2/3x + 6
3y + 6x - 18 = 0
Substituting x = 2 and y = 5 into the equations:
5 = \(\frac{2}{3}\)(2) + 6 (Not satisfied)
3(5) + 6(2) - 18 = 0 (Satisfied)
The point (2,5) is not a solution to this system.
Therefore, the point (2,5) is a solution to system B:
y = -1/2x + 6
y = 3x - 1.
To determine which system of equations the point (2,5) is a solution to, we can substitute the values of x and y into each equation and check if both equations hold true.
Let's start with option A:
1. Substitute x=2 and y=5 into y=x-8:
5 = 2 - 8
5 = -6
The equation is not true, so option A is not the correct answer.
Moving on to option B:
1. Substitute x=2 and y=5 into y=-1/2x+6:
5 = -1/2(2) + 6
5 = -1 + 6
5 = 5
The equation holds true, so option B is a possibility.
Let's check option C:
1. Substitute x=2 and y=5 into y=x+2:
5 = 2 + 2
5 = 4
The equation is not true, so option C is not the correct answer.
Lastly, let's check option D:
1. Substitute x=2 and y=5 into y=2/3x+6:
5 = 2/3(2) + 6
5 = 4/3 + 6
5 = 22/3
The equation is not true, so option D is not the correct answer.
Based on our calculations, the point (2,5) is only a solution to option B:
B. y = -1/2x+6
y = 3x-1