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 system of equations:
y = x + 2
y = x + 5
To determine if the point (2,5) is a solution to a system of equations, we substitute the values of x and y in each equation and check if both equations are satisfied.
1. For the system y=x-8 and 2x+y=7:
Substituting x=2 and y=5 in the first equation:
5 = 2 - 8, which is not true.
Substituting x=2 and y=5 in the second equation:
2(2) + 5 = 7, which is true.
Therefore, the point (2,5) is a solution to the second equation in the system.
2. For the system y=-1/2x+6 and y=3x-1:
Substituting x=2 and y=5 in the first equation:
5 = -1/2(2) + 6, which is true.
Substituting x=2 and y=5 in the second equation:
5 = 3(2) - 1, which is true.
Therefore, the point (2,5) is a solution to both equations in the system.
3. For the system y=x+2 and y=x+5:
Substituting x=2 and y=5 in the first equation:
5 = 2 + 2, which is true.
Substituting x=2 and y=5 in the second equation:
5 = 2 + 5, which is not true.
Therefore, the point (2,5) is not a solution to the second equation in the system.
4. For the system y=2/3x+6 and 3y+6x-18=0:
Substituting x=2 and y=5 in the first equation:
5 = 2/3(2) + 6, which is true.
Substituting x=2 and y=5 in the second equation:
3(5) + 6(2) - 18 = 0, which is true.
Therefore, the point (2,5) is a solution to both equations in the system.
In summary:
- The point (2,5) is a solution to the system of equations:
- y = -1/2x + 6 and y = 3x - 1
- y = 2/3x + 6 and 3y + 6x - 18 = 0
To determine which system of equations the point (2,5) is a solution to, you can substitute the values of x and y from the point into each equation and check if the resulting equation is true.
System 1:
y = x - 8
Substituting (2,5) into the equation: 5 = 2 - 8 is not true.
2x + y = 7
Substituting (2,5) into the equation: 2(2) + 5 = 7 is true.
Therefore, the point (2,5) is a solution to the system of equations 2x + y = 7.
System 2:
y = -1/2x + 6
Substituting (2,5) into the equation: 5 = -1/2(2) + 6 is true.
y = 3x - 1
Substituting (2,5) into the equation: 5 = 3(2) - 1 is not true.
Therefore, the point (2,5) is a solution to the system of equations y = -1/2x + 6.
System 3:
y = x + 2
Substituting (2,5) into the equation: 5 = 2 + 2 is not true.
y = x + 5
Substituting (2,5) into the equation: 5 = 2 + 5 is not true.
Therefore, the point (2,5) is not a solution to the system of equations y = x + 2 and y = x + 5.
System 4:
y = 2/3x + 6
Substituting (2,5) into the equation: 5 = 2/3(2) + 6 is not true.
3y + 6x - 18 = 0
Substituting (2,5) into the equation: 3(5) + 6(2) - 18 = 0 is not true.
Therefore, the point (2,5) is not a solution to the system of equations y = 2/3x + 6 and 3y + 6x - 18 = 0.
In conclusion, the point (2,5) is a solution only to the system of equations 2x + y = 7 and y = -1/2x + 6.