2x+4z=-8
3x+y+5z=2
-x+y-2z=4
I need to solve each system of equations by using the inverse of the coefficient matrix. Are these the correct answers. Thank you
x=24
z=-14
y=0
You can check your answers by plugging those values for x, y, and z into each equation to determine if they work.
To check if the given values for x, y, and z are correct solutions for the system of equations, we can substitute these values back into the original equations and check if they satisfy all of them.
Let's substitute the values x=24, y=0, and z=-14 into the given system of equations:
Equation 1: 2x + 4z = -8
Replacing x=24 and z=-14:
2(24) + 4(-14) = -8
48 - 56 = -8
-8 = -8 (True)
Equation 2: 3x + y + 5z = 2
Replacing x=24, y=0, and z=-14:
3(24) + 0 + 5(-14) = 2
72 - 70 = 2
2 = 2 (True)
Equation 3: -x + y - 2z = 4
Replacing x=24, y=0, and z=-14:
-(24) + 0 - 2(-14) = 4
-24 + 28 = 4
4 = 4 (True)
Since all three equations are satisfied with the given values, x=24, y=0, and z=-14, we can conclude that these values are indeed correct solutions to the given system of equations.
Thus, your answers are correct.