for each ordered pair, determine whether it a solution to the systems of equations
y=4x+7
2x+5y=-9
(x,y) is it a solution? yes/no
(0,7)
(-2,-1)
(3,-3)
(4,6)
To determine whether each ordered pair is a solution to the system of equations, substitute the values of x and y into the equations and check if they are true.
1) (0,7)
y = 4x + 7
7 = 4(0) + 7
7 = 7
Yes, this ordered pair is a solution.
2) (-2,-1)
y = 4x + 7
-1 = 4(-2) + 7
-1 = -8 + 7
-1 = -1
Yes, this ordered pair is a solution.
3) (3,-3)
y = 4x + 7
-3 = 4(3) + 7
-3 = 12 + 7
-3 = 19
No, this ordered pair is not a solution.
4) (4,6)
y = 4x + 7
6 = 4(4) + 7
6 = 16 + 7
6 = 23
No, this ordered pair is not a solution.
So, only the first two ordered pairs (0,7) and (-2,-1) are solutions to the system of equations.
that wasnt correct
Apologies for the incorrect response. Let's revisit the problem and determine whether each ordered pair is a solution to the system of equations.
1) (0,7)
Substituting x = 0 and y = 7 into the equations:
y = 4x + 7
7 = 4(0) + 7
7 = 7
2x + 5y = -9
2(0) + 5(7) = -9
35 = -9
For both equations, the values do not hold true, so the ordered pair (0,7) is not a solution.
2) (-2,-1)
Substituting x = -2 and y = -1 into the equations:
y = 4x + 7
-1 = 4(-2) + 7
-1 = -8 + 7
-1 = -1
2x + 5y = -9
2(-2) + 5(-1) = -9
-4 - 5 = -9
-9 = -9
Both equations hold true, so the ordered pair (-2,-1) is a solution.
3) (3,-3)
Substituting x = 3 and y = -3 into the equations:
y = 4x + 7
-3 = 4(3) + 7
-3 = 12 + 7
-3 = 19
2x + 5y = -9
2(3) + 5(-3) = -9
6 - 15 = -9
-9 = -9
Both equations hold true, so the ordered pair (3,-3) is a solution.
4) (4,6)
Substituting x = 4 and y = 6 into the equations:
y = 4x + 7
6 = 4(4) + 7
6 = 16 + 7
6 = 23
2x + 5y = -9
2(4) + 5(6) = -9
8 + 30 = -9
38 = -9
For both equations, the values do not hold true, so the ordered pair (4,6) is not a solution.
In summary, the solutions to the system of equations are (-2,-1) and (3,-3), while (0,7) and (4,6) are not solutions.