Question

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine if the point (2,5) is a solution to a system of equations, we can substitute the x and y values into each equation and see if they are true.

Let's try each system of equations:

A. y=x-8, 2x+y=7
Substituting x=2 and y=5 into the first equation:
5=2-8
This is not true, so (2,5) is not a solution to the first equation.
Substituting x=2 and y=5 into the second equation:
2(2)+5=7
This is true, so (2,5) is a solution to the second equation.

B. y=-1/2x+6, y=3x-1
Substituting x=2 and y=5 into the first equation:
5=-1/2(2)+6
This is true, so (2,5) is a solution to the first equation.
Substituting x=2 and y=5 into the second equation:
5=3(2)-1
This is not true, so (2,5) is not a solution to the second equation.

C. y=x+2, y=x+5
Substituting x=2 and y=5 into the first equation:
5=2+2
This is not true, so (2,5) is not a solution to the first equation.
Substituting x=2 and y=5 into the second equation:
5=2+5
This is true, so (2,5) is a solution to the second equation.

D. y=2/3x+6, 3y+6x-18=0
Substituting x=2 and y=5 into the first equation:
5=2/3(2)+6
This is not true, so (2,5) is not a solution to the first equation.
Substituting x=2 and y=5 into the second equation:
3(5)+6(2)-18=0
15+12-18=0
This is true, so (2,5) is a solution to the second equation.

The point (2,5) is a solution to systems B and D of equations.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To determine which system of equations the point (2,5) is a solution to, we need to substitute the x and y values into each equation and see if they satisfy both equations.

A. y=x-8, 2x+y=7:
Substituting the values x=2 and y=5 into the first equation:
5 = 2 - 8
This is not true. Therefore, (2,5) is not a solution to this system.

B. y=-1/2x+6, y=3x-1:
Substituting the values x=2 and y=5 into the first equation:
5 = -1/2(2) + 6
5 = -1 + 6
This is true. Proceeding to the second equation:
5 = 3(2) - 1
5 = 6 - 1
This is also true. Therefore, (2,5) is a solution to this system.

C. y=x+2, y=x+5:
Substituting the values x=2 and y=5 into the first equation:
5 = 2 + 2
5 = 4
This is not true. Therefore, (2,5) is not a solution to this system.

D. y=2/3x+6, 3y+6x-18=0:
Substituting the values x=2 and y=5 into the first equation:
5 = 2/3(2) + 6
5 = 4/3 + 6
This is not true. Therefore, (2,5) is not a solution to this system.

Based on the above analysis, the point (2,5) is a solution to the system of equations described in option B: y=-1/2x+6, y=3x-1.

Answer 3

[AI-generated answer — Explain Bot]

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 of the system and check if both equations are satisfied.

Let's go through the options one by one:

A. y = x - 8 and 2x + y = 7
Substituting x = 2 and y = 5 into the first equation:
5 = 2 - 8
This is false, as 5 does not equal -6.
Substituting x = 2 and y = 5 into the second equation:
2(2) + 5 = 7
This is true, as 4 + 5 equals 7.
Since one of the equations is not satisfied, option A is not the correct answer.

B. y = -1/2x + 6 and y = 3x - 1
Substituting x = 2 and y = 5 into the first equation:
5 = -1/2(2) + 6
This is true, as 5 equals 5.
Substituting x = 2 and y = 5 into the second equation:
5 = 3(2) - 1
This is true, as 5 equals 5.
Both equations are satisfied, so option B is a potential solution.

C. y = x + 2 and y = x + 5
Substituting x = 2 and y = 5 into the first equation:
5 = 2 + 2
This is true, as 5 equals 4.
Substituting x = 2 and y = 5 into the second equation:
5 = 2 + 5
This is true, as 5 equals 7.
Both equations are not satisfied, so option C is not the correct answer.

D. y = 2/3x + 6 and 3y + 6x - 18 = 0
Substituting x = 2 and y = 5 into the first equation:
5 = 2/3(2) + 6
This is true, as 5 equals 5.
Substituting x = 2 and y = 5 into the second equation:
3(5) + 6(2) - 18 = 0
This is true, as 15 + 12 - 18 equals 9.
Both equations are satisfied, so option D is a potential solution.

After evaluating all the options, we find that the point (2,5) is a solution to both options B and D. Therefore, options B and D are the correct answers.