The point (5, -3) is a solution to which system of equations?
y = x + 2
y = x + 5
y = -1/2x + 6
y = 3x - 1
y = x - 8
2x + y = 7
The point (5, -3) is a solution to the system of equations:
y = x + 2
y = x + 5
To determine which system of equations the point (5, -3) is a solution to, we need to substitute the x and y values into each equation and check if both equations are satisfied.
1. For the first system of equations:
y = x + 2 ---(1)
y = x + 5 ---(2)
Substitute x = 5 and y = -3 into equations (1) and (2):
(1) -3 = 5 + 2 => -3 = 7 [Not satisfied]
(2) -3 = 5 + 5 => -3 = 10 [Not satisfied]
Therefore, (5, -3) is not a solution to the first system of equations.
2. For the second system of equations:
y = -1/2x + 6 ---(3)
y = 3x - 1 ---(4)
Substitute x = 5 and y = -3 into equations (3) and (4):
(3) -3 = -1/2(5) + 6 => -3 = -5/2 + 6 => -3 = 7/2 [Not satisfied]
(4) -3 = 3(5) - 1 => -3 = 15 - 1 => -3 = 14 [Not satisfied]
Therefore, (5, -3) is not a solution to the second system of equations.
3. For the third system of equations:
y = x - 8 ---(5)
2x + y = 7 ---(6)
Substitute x = 5 and y = -3 into equations (5) and (6):
(5) -3 = 5 - 8 => -3 = -3 [Satisfied]
(6) 2(5) + (-3) = 7 => 7 = 7 [Satisfied]
Therefore, (5, -3) is a solution to the third system of equations.
Hence, the point (5, -3) is a solution to the system of equations represented by equations (5) and (6):
y = x - 8
2x + y = 7
To determine if the point (5, -3) is a solution to a system of equations, we will substitute the values of x and y into each equation and check if the equations are satisfied.
For the first system of equations:
1. y = x + 2
2. y = x + 5
Substituting x = 5 and y = -3 into equation 1:
-3 = 5 + 2 evaluates to -3 = 7, which is not true.
Substituting x = 5 and y = -3 into equation 2:
-3 = 5 + 5 evaluates to -3 = 10, which is also not true.
Therefore, the point (5, -3) is not a solution to the first system of equations.
Moving on to the second system of equations:
1. y = -1/2x + 6
2. y = 3x - 1
Substituting x = 5 and y = -3 into equation 1:
-3 = -1/2 * 5 + 6 evaluates to -3 = -5/2 + 6, which is true.
Substituting x = 5 and y = -3 into equation 2:
-3 = 3 * 5 - 1 evaluates to -3 = 15 - 1, which is also true.
Therefore, the point (5, -3) is a solution to the second system of equations.
Lastly, let's consider the third system of equations:
1. y = x - 8
2. 2x + y = 7
Substituting x = 5 and y = -3 into equation 1:
-3 = 5 - 8 evaluates to -3 = -3, which is true.
Substituting x = 5 and y = -3 into equation 2:
2(5) + (-3) = 7 evaluates to 10 - 3 = 7, which is true.
Therefore, the point (5, -3) is also a solution to the third system of equations.
In conclusion, the point (5, -3) is a solution to the second and third systems of equations.