Determine if the ordered pair is a solution to the system.
-5x - 7y= 4
y= 1/2 x - 1
a. (2,2) b. (2, -2)
The solution should satisfy both Eqs:
-5x - 7 = 4. (2,2).
-5*2 - 7*2 = -24. Therefore, (2,2) is not a solution.
Test the other point in both Eqs.
You'll find that neither point satisfies
both Eqs.
To determine if the ordered pair is a solution to the system, substitute the values of x and y into both equations and check if the equations are true.
Let's start with the first equation: -5x - 7y = 4.
a. (2,2):
Substituting the values x = 2 and y = 2 into the equation:
-5(2) - 7(2) = 4
-10 - 14 = 4
-24 = 4
Since -24 is not equal to 4, the first equation is not true for the ordered pair (2,2).
Now, let's move to the second equation: y = 1/2x - 1.
a. (2,2):
Substituting the values x = 2 and y = 2 into the equation:
2 = 1/2(2) - 1
2 = 1 - 1
2 = 0
Since 2 is not equal to 0, the second equation is not true for the ordered pair (2,2).
Therefore, the ordered pair (2,2) is not a solution to the system.
To determine if an ordered pair is a solution to a system of equations, you need to substitute the values of the ordered pair into the system and see if both equations remain true.
Let's start with the given system of equations:
-5x - 7y = 4 (Equation 1)
y = 1/2x - 1 (Equation 2)
We will substitute the values of the ordered pair (2, 2) into both equations and check if they are still true.
For Equation 1:
-5x - 7y = 4
Substituting x = 2 and y = 2, we have:
-5(2) - 7(2) = 4
-10 - 14 = 4
-24 = 4
Since -24 is not equal to 4, Equation 1 is not true when (x, y) = (2, 2).
Now let's check Equation 2:
y = 1/2x - 1
Substituting x = 2 and y = 2, we have:
2 = 1/2(2) - 1
2 = 1 - 1
2 = 0
Since 2 is not equal to 0, Equation 2 is not true when (x, y) = (2, 2).
Therefore, the ordered pair (2, 2) is not a solution to the given system of equations.