Determine which of the following ordered pairs is a solution of the given system of equations.
y=2x−5
y=4x−7
A (−1,3)
B (1,−3)
C (0,−5)
D (2,2)
To determine if an ordered pair is a solution of the system of equations, we need to substitute the values of x and y into both equations and see if the equations are true.
Let's test each ordered pair:
A) (-1, 3)
Substituting x = -1 and y = 3 into the first equation:
3 = 2(-1) - 5
3 = -2 - 5
3 ≠ -7
Substituting x = -1 and y = 3 into the second equation:
3 = 4(-1) - 7
3 = -4 - 7
3 ≠ -11
Therefore, (-1, 3) is not a solution of the system of equations.
B) (1, -3)
Substituting x = 1 and y = -3 into the first equation:
-3 = 2(1) - 5
-3 = 2 - 5
-3 ≠ -3
Substituting x = 1 and y = -3 into the second equation:
-3 = 4(1) - 7
-3 = 4 - 7
-3 ≠ -3
Therefore, (1, -3) is not a solution of the system of equations.
C) (0, -5)
Substituting x = 0 and y = -5 into the first equation:
-5 = 2(0) - 5
-5 = 0 - 5
-5 = -5
Substituting x = 0 and y = -5 into the second equation:
-5 = 4(0) - 7
-5 = 0 - 7
-5 = -7
Both equations are true when x = 0 and y = -5 in this pair.
Therefore, (0, -5) is a solution of the system of equations.
D) (2, 2)
Substituting x = 2 and y = 2 into the first equation:
2 = 2(2) - 5
2 = 4 - 5
2 ≠ -1
Substituting x = 2 and y = 2 into the second equation:
2 = 4(2) - 7
2 = 8 - 7
2 ≠ 1
Therefore, (2, 2) is not a solution of the system of equations.
In conclusion, the only ordered pair that is a solution of the system of equations is C) (0, -5).