Answer:
Q3: x = 4, y = 4, z = 4
Q4: x = 6, y = 0, z = -4
Step-by-step explanation:
Question 3: Simultaneous equations requires us to solve for x, y and z.
Since all three equations have a z in them, I will first solve for z.
Substitute in the first and third equation into the second equation.
First equation: x = 5z - 16
Second Equation: -4x + 4y - 5z = -20
Third equation: y = -z + 8
Substituting in x = 5z - 16 and y = -z + 8 for the x and y in the second equation.
-4(5z - 16) + 4(-z + 8) - 5z = -20
Expand
-20z + 64 - 4z + 32 - 5z = -20
Simplify and solve for z by putting all the numbers on one side and all the z's on the other side of the equals
-20z - 4z - 5z = -20 - 32 - 64
-29z = -116
z = -116/-29
z = 4
Substitute in this z value into the first and last equation and then solve for x and y
x = 5z - 16
x = 5(4) - 16
x = 20 - 16
x = 4
And
y = -z + 8
y = -(4) + 8
y = 4 (Its just a coincidence that they all equal to 4, I promise)
Question 5: A little bit harder of a question. Since the first and second equation both only have y and z, we can solve it using the elimination method.
Rearrange them so that the letters are on one side and numbers on the other side.
First equation: y + 6z = -24
Second equation: z + 2y = -4
I will choose to eliminate the y (You can choose either or)
Multiply the first equation by 2
2(y + 6z = -24)
2y + 12z = -48
Now that 2y is in both equations, we can minus one equation from the other to eliminate the y (I will minus the second from the first)
First Eq: 2y + 12z = -48
Second Eq: z + 2y = -4
2y - 2y = 0y
12z - z = 11z
-48 - (-4) = -44
Type these answers into a new equation
0y + 11z = - 44
Since y is 0, ignore it. Solve for z
11z = -44
z = -44/11
z = - 4
Substitute our z into either the first or second equation and solve for y (It doesnt matter which one you choose, I just did the second equation)
z + 2y = -4
(-4) + 2y = -4
2y = -4 + 4
2y = 0
y = 0
Substitute in our y and z values into the third equation and solve for x
-6x - 6y - 6z = -12
-6x - 6(0) - 6(-4) = -12
-6x - 0 + 24 = -12
-6x = -12 - 24
-6x = -36
x = -36/-6
x = 6
