I do not know how to do this problem can someone help me please. Thank you.
Determine if the given ordered triple below is a solution. (3, 3, -5)
x + 9y = 30
2x - 8y = -18
5y + 2z = 5
To determine if the given ordered triple (3, 3, -5) is a solution for the system of equations, you need to substitute the values of x, y, and z into each equation and check if the equations are satisfied.
Let's start by substituting the values into the first equation:
x + 9y = 30
Replace x with 3 and y with 3:
3 + 9(3) = 30
3 + 27 = 30
30 = 30
Since the equation is true, (3, 3, -5) satisfies the first equation.
Next, let's substitute the values into the second equation:
2x - 8y = -18
Replace x with 3 and y with 3:
2(3) - 8(3) = -18
6 - 24 = -18
-18 = -18
Again, the equation is true, so (3, 3, -5) satisfies the second equation as well.
Lastly, substitute the values into the third equation:
5y + 2z = 5
Replace y with 3 and z with -5:
5(3) + 2(-5) = 5
15 - 10 = 5
5 = 5
The equation holds true, which means that (3, 3, -5) also satisfies the third equation.
As (3, 3, -5) satisfies all three equations in the system, it is indeed a solution.