The point (2,5) is a solution to which system of equations?
y=x-8
2x+y=7
y=-1/2x+6
y=3x-1
y=x+2
y=x+5
y=2/3x+6
3y+6x-18=0
The point (2,5) is a solution to the following system of equations:
- y = x+2
- y = x+5
To determine if the point (2,5) is a solution to a system of equations, you can substitute the x and y values into both equations and see if they satisfy each equation.
Let's check each system of equations:
1. y = x - 8
2x + y = 7
Substituting x = 2 and y = 5:
y = 2 - 8
y = -6
2x + y = 7
2(2) + 5 = 7
4 + 5 = 7
9 = 7
The point (2,5) does not satisfy this system of equations.
2. y = -1/2x + 6
y = 3x - 1
Substituting x = 2 and y = 5:
5 = -1/2(2) + 6
5 = -1 + 6
5 = 5
5 = 3(2) - 1
5 = 6 - 1
5 = 5
The point (2,5) is a solution to this system of equations.
3. y = x + 2
y = x + 5
Substituting x = 2 and y = 5:
5 = 2 + 2
5 = 4
5 = 2 + 5
5 = 7
The point (2,5) does not satisfy this system of equations.
4. y = 2/3x + 6
3y + 6x - 18 = 0
Substituting x = 2 and y = 5:
5 = 2/3(2) + 6
5 = 4/3 + 6
5 = 22/3
3(5) + 6(2) - 18 = 0
15 + 12 - 18 = 0
27 - 18 = 0
9 = 0
The point (2,5) does not satisfy this system of equations.
Therefore, the point (2,5) is only a solution to the system of equations y = -1/2x + 6 and 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 see which system yields a true statement.
For the first system of equations:
1. Substitute x=2 and y=5 into the first equation:
5 = 2 - 8
The statement is not true.
2. Substitute x=2 and y=5 into the second equation:
2(2) + 5 = 7
The statement is true.
Therefore, the point (2,5) is a solution to the second system of equations:
2x + y = 7.
Let's verify the remaining systems of equations:
For the second system of equations:
1. Substitute x=2 and y=5 into the first equation:
5 ≠ -1/2(2) + 6
The statement is not true.
2. Substitute x=2 and y=5 into the second equation:
5 ≠ 3(2) - 1
The statement is not true.
For the third system of equations:
1. Substitute x=2 and y=5 into the first equation:
7 ≠ 2 + 2
The statement is not true.
2. Substitute x=2 and y=5 into the second equation:
5 ≠ 2 + 5
The statement is not true.
For the fourth system of equations:
1. Substitute x=2 and y=5 into the first equation:
5 ≠ 2/3(2) + 6
The statement is not true.
2. Substitute x=2 and y=5 into the second equation:
3(5) + 6(2) - 18 ≠ 0
The statement is not true.
Based on our analysis, the point (2,5) is a solution to only the second system of equations:
2x + y = 7.