The point (2,5) is a solution to which system of equations?(1 point)
Responses
y=x-8 2x+y=7
y=- 1/2 x +6 y=3x=1
y=x+2 y=x+5
y=2/3 x + 6 3y+6x-18=0
To determine which system of equations the point (2,5) is a solution to, substitute the values x=2 and y=5 into each equation and see if the equations are satisfied:
1) y=x-8
5=2-8 => False
This equation is not satisfied for the point (2,5).
2) 2x+y=7
2(2)+5=7
4+5=7
9=7 => False
This equation is not satisfied for the point (2,5).
3) y=-1/2x+6
5=-1/2(2)+6
5=-1+6
5=5 => True
This equation is satisfied for the point (2,5).
4) y=3x=1
This equation contains a typographical error with two equal signs. Please check the equation again.
Therefore, the point (2,5) is a solution to the system of equations:
y=-1/2x+6
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 the equations hold true.
1. y=x-8
Substituting x = 2 and y = 5, we get: 5 = 2 - 8, which is not true.
2. 2x+y=7
Substituting x = 2 and y = 5, we get: 2(2) + 5 = 7, which is true.
3. y=- 1/2 x + 6
Substituting x = 2 and y = 5, we get: 5 = -1/2(2) + 6, which is true.
4. y=x+2
Substituting x = 2 and y = 5, we get: 5 = 2 + 2, which is true.
5. y=2/3 x + 6
Substituting x = 2 and y = 5, we get: 5 = 2/3(2) + 6, which is not true.
Therefore, the point (2,5) is a solution to the system of equations:
- 2x+y=7
- y=- 1/2 x + 6
- y=x+2
To find out if the point (2,5) is a solution to a system of equations, we need to substitute the values of x and y into each equation and see if they hold true.
Let's go through each system of equations:
1. y = x - 8
2x + y = 7
Substituting x=2 and y=5 into the first equation:
5 = 2 - 8
This equation is not true, so the point (2,5) is not a solution to the first system of equations.
Substituting x=2 and y=5 into the second equation:
2(2) + 5 = 7
This equation is true, so the point (2,5) is a solution to the second system of equations.
2. y = -1/2 x + 6
y = 3x = 1
The second equation has a typo with two equal signs. Assuming it is a typo and should be y = 3x - 1, we can proceed:
Substituting x=2 and y=5 into the first equation:
5 = -1/2(2) + 6
This equation is not true, so the point (2,5) is not a solution to the first system of equations.
Substituting x=2 and y=5 into the second equation:
5 = 3(2) - 1
This equation is not true, so the point (2,5) is not a solution to the second system of equations.
3. y = x + 2
y = x + 5
Substituting x=2 and y=5 into the first equation:
5 = 2 + 2
This equation is not true, so the point (2,5) is not a solution to the first system of equations.
Substituting x=2 and y=5 into the second equation:
5 = 2 + 5
This equation is not true, so the point (2,5) is not a solution to the second system of equations.
4. y = 2/3 x + 6
3y + 6x - 18 = 0
Substituting x=2 and y=5 into the first equation:
5 = 2/3(2) + 6
This equation is not true, so the point (2,5) is not a solution to the first system of equations.
Substituting x=2 and y=5 into the second equation:
3(5) + 6(2) - 18 = 0
This equation is true, so the point (2,5) is a solution to the second system of equations.
In conclusion, the point (2,5) is a solution to the second system of equations:
2x + y = 7
3y + 6x - 18 = 0