For each ordered pair, determine whether it is a solution to the system of equations.
y=4x-3
8x-2y=6
(x,y) Is it a solution?
Yes No
(-2,-11) O O
(5,17) O O
(3,-1) O O
(0,7) O O
To determine whether each ordered pair is a solution to the system of equations, we need to substitute the values of x and y into each equation and see if the equations hold true.
For the first ordered pair (-2, -11):
1) Substitute x = -2 and y = -11 into the equation y = 4x - 3:
-11 = 4(-2) - 3
-11 = -8 - 3
-11 = -11
The equation holds true.
2) Substitute x = -2 and y = -11 into the equation 8x - 2y = 6:
8(-2) - 2(-11) = 6
-16 + 22 = 6
6 = 6
The equation also holds true.
For the second ordered pair (5, 17):
1) Substitute x = 5 and y = 17 into the equation y = 4x - 3:
17 = 4(5) - 3
17 = 20 - 3
17 = 17
The equation holds true.
2) Substitute x = 5 and y = 17 into the equation 8x - 2y = 6:
8(5) - 2(17) = 6
40 - 34 = 6
6 = 6
The equation also holds true.
For the third ordered pair (3, -1):
1) Substitute x = 3 and y = -1 into the equation y = 4x - 3:
-1 = 4(3) - 3
-1 = 12 - 3
-1 = 9
The equation does not hold true.
2) Substitute x = 3 and y = -1 into the equation 8x - 2y = 6:
8(3) - 2(-1) = 6
24 + 2 = 6
26 = 6
The equation does not hold true.
For the fourth ordered pair (0, 7):
1) Substitute x = 0 and y = 7 into the equation y = 4x - 3:
7 = 4(0) - 3
7 = 0 - 3
7 = -3
The equation does not hold true.
2) Substitute x = 0 and y = 7 into the equation 8x - 2y = 6:
8(0) - 2(7) = 6
0 - 14 = 6
-14 = 6
The equation does not hold true.
To summarize:
- The ordered pair (-2, -11) is a solution to the system of equations.
- The ordered pair (5, 17) is a solution to the system of equations.
- The ordered pair (3, -1) is not a solution to the system of equations.
- The ordered pair (0, 7) is not a solution to the system of equations.