Which ordered pair is a solution of the system of equations y=x^2-x-20 and y=3x-15?
a. (-5,-30)
b. (-1,-18)
c. (0,5)
d. (5,-1)
When I solved the system of equations I got 5 and -1. What do I do next?
If x = 5
y = 0, not one of the solutions listed
If x = -1. y = -3-15 = -18
so
(-1,-18) is what they are looking for.
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Well, congratulations on solving the system of equations! But remember, you still need to check if those values satisfy both equations. It's like testing if a new pizza recipe is delicious or not.
Let's test the first value, 5. If we plug it into the first equation, we get y = (5)^2 - (5) - 20. Simplifying that gives y = 25 - 5 - 20, which equals 0. Now, let's check the second equation: if we substitute x = 5, we get y = 3(5) - 15, which simplifies to y = 15 - 15, resulting in y = 0 again.
So, the point (5, 0) is a valid solution for the system of equations. Now, let's check the other value, -1. Substituting that into the first equation gives us y = (-1)^2 - (-1) - 20, which simplifies to y = 1 + 1 - 20, or y = -18. Now, let's check the second equation: if we substitute x = -1, we get y = 3(-1) - 15, which simplifies to y = -3 - 15, resulting in y = -18 again.
Therefore, both values satisfy the system of equations. So, the correct answer is (d) (5, -1). Keep up the good work and don't be clowning around with your answers!
To determine which ordered pair is a solution of the system of equations, you need to substitute each value for x into the equations and check if the resulting y-values satisfy both equations.
For the first option, (-5,-30):
Substituting x = -5 into the first equation:
y = (-5)^2 - (-5) - 20
y = 25 + 5 - 20
y = 10
Substituting x = -5 into the second equation:
y = 3(-5) - 15
y = -15
So, the first option does not satisfy both equations since y is not equal to both 10 and -15.
You can repeat this process for the remaining options using their respective x-values. By substituting x = -1, x = 0, and x = 5 into both equations, you can determine if the resulting y-values satisfy both equations.
For example, for the second option (-1,-18):
Substituting x = -1 into the first equation:
y = (-1)^2 - (-1) - 20
y = 1 + 1 - 20
y = -18
Substituting x = -1 into the second equation:
y = 3(-1) - 15
y = -18
Since both equations yield y = -18, the second option (-1,-18) is a solution to the system of equations.
You can continue to try this method for the other options until you find the solution that satisfies both equations.