Which ordered pair is for the solution.
y=3x-5
y=1/2x
(6,3),(1,-2),(2,1),(-2,1)
well, did you try plugging in the values?
is 3 = 3*6-5? No
so, look for one pair which works in both equations.
To find the ordered pair that represents the solution to the system of equations, you need to substitute the x and y values of each ordered pair into both equations and check if the values satisfy the equations.
Let's go through each ordered pair one by one and plug in the values into the equations:
1. For the ordered pair (6,3):
Substituting x=6 and y=3 into the first equation:
y = 3x - 5
3 = 3(6) - 5
3 = 18 - 5
3 = 13, which is not true.
Substituting x=6 and y=3 into the second equation:
y = (1/2)x
3 = (1/2)(6)
3 = 3, which is true.
The ordered pair (6,3) satisfies the second equation, but not the first equation. Therefore, it is not the solution.
2. For the ordered pair (1,-2):
Substituting x=1 and y=-2 into the first equation:
y = 3x - 5
-2 = 3(1) - 5
-2 = 3 - 5
-2 = -2, which is true.
Substituting x=1 and y=-2 into the second equation:
y = (1/2)x
-2 = (1/2)(1)
-2 = 1/2, which is not true.
The ordered pair (1,-2) satisfies the first equation, but not the second equation. Therefore, it is also not the solution.
3. For the ordered pair (2,1):
Substituting x=2 and y=1 into the first equation:
y = 3x - 5
1 = 3(2) - 5
1 = 6 - 5
1 = 1, which is true.
Substituting x=2 and y=1 into the second equation:
y = (1/2)x
1 = (1/2)(2)
1 = 1, which is true.
The ordered pair (2,1) satisfies both equations. Therefore, it is a valid solution.
4. For the ordered pair (-2,1):
Substituting x=-2 and y=1 into the first equation:
y = 3x - 5
1 = 3(-2) - 5
1 = -6 - 5
1 = -11, which is not true.
Substituting x=-2 and y=1 into the second equation:
y = (1/2)x
1 = (1/2)(-2)
1 = -1, which is not true.
The ordered pair (-2,1) does not satisfy either equation. Therefore, it is not the solution.
In conclusion, the only ordered pair that satisfies both equations is (2,1).