The point (2,5) is a solution to which system of equations?(1 point)
Responses
A. 7=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
The correct answer is B. y=-1/2x+6 and y=3x-1. When we substitute x = 2 and y = 5 into these equations, we get:
y = -1/2(2) + 6
y = -1 + 6
y = 5
y = 3(2) - 1
y = 6 - 1
y = 5
Both equations are satisfied, which means (2, 5) is a solution to this system of equations.
To find which system of equations the point (2,5) is a solution to, we need to substitute the values of x and y from the point into each system and see which ones satisfy the equations.
Let's substitute x=2 and y=5 in each system of equations:
A. 7=x-8 (2x+y=7)
7=2-8
7=-6
This is not true, so (2,5) is not a solution to this system.
B. y=-1/2x+6 (y=3x-1)
5=-1/2(2)+6
5=-1+6
5=5
This is true, so (2,5) is a solution to this system.
C. y=x+2 (y=x+5)
5=2+2
5=4
This is not true, so (2,5) is not a solution to this system.
D. y=2/3x+6 (3y+6x-18=0)
5=2/3(2)+6
5=4/3+6
5=22/3
This is not true, so (2,5) is not a solution to this system.
Therefore, the point (2,5) is a solution to the system of equations: y=-1/2x+6 and y=3x-1, which corresponds to option B.
To find out which system of equations is satisfied by the point (2,5), we need to substitute the values of x and y into each equation and check if the equation is true.
Let's check each equation one by one:
A. 7 = x - 8
Substituting the values x=2 and y=5, we have 7 = 2 - 8, which is not true. So this system is not satisfied.
B. y = -1/2x + 6
Substituting the values x=2 and y=5, we have 5 = -1/2(2) + 6, which is true. So this system is satisfied.
C. y = x + 2
Substituting the values x=2 and y=5, we have 5 = 2 + 2, which is not true. So this system is not satisfied.
D. y = 2/3x + 6
Substituting the values x=2 and y=5, we have 5 = 2/3(2) + 6, which is not true. So this system is not satisfied.
So, the point (2,5) is a solution to the system of equations B:
y = -1/2x + 6
y = 3x - 1.