For each ordered pair, determine whether it is a solution to the system of equations.
y=4x+7
-7x+3y=1
(x,y) Is it a solution?
Yes No
(0,-8) O O
(2,5) O O
(-4,-9) O O
(-1,3) O O
For each ordered pair, we can substitute the values of x and y into the equations to check if they satisfy the equations.
For the first ordered pair (0, -8),
y = 4x + 7
-8 = 4(0) + 7
-8 = 7
This is not true, so (0, -8) is not a solution to the system of equations.
For the second ordered pair (2, 5),
y = 4x + 7
5 = 4(2) + 7
5 = 8 + 7
5 = 15
Again, this is not true, so (2, 5) is not a solution to the system of equations.
For the third ordered pair (-4, -9),
y = 4x + 7
-9 = 4(-4) + 7
-9 = -16 + 7
-9 = -9
This is true, so (10, -9) is a solution to the system of equations.
For the fourth ordered pair (-1, 3),
y = 4x + 7
3 = 4(-1) + 7
3 = -4 + 7
3 = 3
This is true, so (-1, 3) is a solution to the system of equations.
Therefore, the solutions are:
(0, -8) - No
(2, 5) - No
(-4, -9) - Yes
(-1, 3) - Yes
you sure
Apologies for the incorrect response. Let me recalculate the solutions:
For the first ordered pair (0, -8):
y = 4x + 7
-8 = 4(0) + 7
-8 = 7 - not true
-7x + 3y = 1
-7(0) + 3(-8) = 1
-24 = 1 - not true
So, (0, -8) is not a solution to the system of equations.
For the second ordered pair (2, 5):
y = 4x + 7
5 = 4(2) + 7
5 = 8 + 7 - not true
-7x + 3y = 1
-7(2) + 3(5) = 1
-14 + 15 = 1 - true
So, (2, 5) is not a solution to the system of equations.
For the third ordered pair (-4, -9):
y = 4x + 7
-9 = 4(-4) + 7
-9 = -16 + 7 - true
-7x + 3y = 1
-7(-4) + 3(-9) = 1
28 - 27 = 1 - true
So, (-4, -9) is a solution to the system of equations.
For the fourth ordered pair (-1, 3):
y = 4x + 7
3 = 4(-1) + 7
3 = -4 + 7 - true
-7x + 3y = 1
-7(-1) + 3(3) = 1
7 + 9 = 1 - not true
So, (-1, 3) is not a solution to the system of equations.
Therefore, the correct solutions are:
(0, -8) - No
(2, 5) - No
(-4, -9) - Yes
(-1, 3) - No
To determine whether an ordered pair is a solution to a system of equations, you need to substitute the values of x and y in the equations and check if they satisfy both of them.
Here's how we can check each ordered pair:
1) (0, -8)
- Substituting x = 0 and y = -8 in the first equation:
y = 4x + 7
-8 = 4(0) + 7
-8 = 7
This is not true, so (0, -8) is not a solution to the system of equations.
2) (2, 5)
- Substituting x = 2 and y = 5 in the first equation:
y = 4x + 7
5 = 4(2) + 7
5 = 8 + 7
5 = 15
This is not true, so (2, 5) is not a solution to the system of equations.
3) (-4, -9)
- Substituting x = -4 and y = -9 in the first equation:
y = 4x + 7
-9 = 4(-4) + 7
-9 = -16 + 7
-9 = -9
This equation is true.
- Substituting x = -4 and y = -9 in the second equation:
-7x + 3y = 1
-7(-4) + 3(-9) = 1
28 - 27 = 1
1 = 1
This equation is also true.
Since both equations are true, (-4, -9) is a solution to the system of equations.
4) (-1, 3)
- Substituting x = -1 and y = 3 in the first equation:
y = 4x + 7
3 = 4(-1) + 7
3 = -4 + 7
3 = 3
This equation is true.
- Substituting x = -1 and y = 3 in the second equation:
-7x + 3y = 1
-7(-1) + 3(3) = 1
7 + 9 = 1
16 = 1
This equation is not true, so (-1, 3) is not a solution to the system of equations.
To summarize:
- (0, -8) is not a solution.
- (2, 5) is not a solution.
- (-4, -9) is a solution.
- (-1, 3) is not a solution.