I need to solve the system of equations letting z be the parameter

7x+y+7z=-12
-3x+4y+6z=-1

This is suppose to be the right answer
{-47/31-22/31z-43/31-63/31z,z}

I keep getting
{-22/31-47-31z-63/31-43/31z,z}

7x+y+7z=-12

-3x+4y+6z=-1

28x+4y+28z=-48
-3x+4y+6z=-1
subtract bottom eq
31x-22z=-47
x= -47/31 +22/31 z

You can do the x.

7x+4y=-16

6x-4y=-36

To solve the system of equations, you can use the method of substitution or elimination. In this case, we can use the method of elimination to find the solution.

First, let's write the system of equations in standard form:

7x + y + 7z = -12 --> 7x + y + 7z + 12 = 0 (Equation 1)
-3x + 4y + 6z = -1 --> -3x + 4y + 6z + 1 = 0 (Equation 2)

To use the method of elimination, we need to eliminate one variable at a time. Let's eliminate x first.

To eliminate x, multiply Equation 1 by 3 and Equation 2 by 7:

21x + 3y + 21z + 36 = 0 (Equation 1 multiplied by 3)
-21x + 28y + 42z + 7 = 0 (Equation 2 multiplied by 7)

Now, add the two equations together to eliminate x:

(21x - 21x) + (3y + 28y) + (21z + 42z) + (36 + 7) = 0

Simplifying the equation, we get:

31y + 63z + 43 = 0

This gives us a new equation, which we will call Equation 3:

31y + 63z + 43 = 0 --> 31y + 63z = -43 (Equation 3)

Now, we have two equations:

31y + 63z = -43 (Equation 3)
-3x + 4y + 6z + 1 = 0 (Equation 2)

To eliminate y, multiply Equation 3 by 4 and Equation 2 by 31:

124y + 252z = -172 (Equation 3 multiplied by 4)
-93x + 124y + 186z + 31 = 0 (Equation 2 multiplied by 31)

Now, subtract Equation 3 from Equation 2 to eliminate y:

(-93x + 124y) - (124y + 252z) + (186z + 31 - (-172)) = 0

Simplifying the equation, we get:

-93x - 66z + 203 = 0

This gives us a new equation, which we will call Equation 4:

-93x - 66z + 203 = 0 --> -93x - 66z = -203 (Equation 4)

Now, we have two equations:

-93x - 66z = -203 (Equation 4)
31y + 63z = -43 (Equation 3)

To solve for x, we can eliminate z. Multiply Equation 4 by 63 and Equation 3 by 66:

-5859x - 4158z = -12849 (Equation 4 multiplied by 63)
2046y + 4158z = -2838 (Equation 3 multiplied by 66)

Now, add the two equations together to eliminate z:

(-5859x + 2046y) + (-4158z + 4158z) + (-12849 + -2838) = 0

Simplifying the equation, we get:

-5859x + 2046y - 15687 = 0

This gives us a new equation, which we will call Equation 5:

-5859x + 2046y = 15687 (Equation 5)

Now, we have two equations:

-5859x + 2046y = 15687 (Equation 5)
31y + 63z = -43 (Equation 3)

Let z be the parameter, so we can solve for x and y in terms of z.

Starting with Equation 5:

-5859x + 2046y = 15687

Rearranging the equation, we get:

x = (2046y - 15687) / -5859 (Equation 6)

Next, substitute Equation 6 into Equation 3:

31y + 63z = -43

Substituting x from Equation 6 into Equation 3:

31y + 63z = -43
31y + 63z = -43 + 43x

Since x = (2046y - 15687) / -5859:

31y + 63z = -43 + 43((2046y - 15687) / -5859)

Now, simplify the equation:

31y + 63z = -43 - 43(2046y - 15687) / 5859

Multiply through by 5859 to clear the fraction:

5859(31y + 63z) = -5859(-43) - 43(2046y - 15687)

After simplifying, we get:

5859(31y) + 5859(63z) = 251787 + 306381y - 603009

Combining like terms, we have:

5859(31y) + 5859(63z) = 306381y - 351222

Divide through by 31 to isolate y:

189y + 63z = 306381y - 351222

Rearranging the equation, we get:

-299y + 63z = -351222

Finally, isolate y to get the expression in terms of z:

-299y = -351222 - 63z

Divide through by -299:

y = (-351222 - 63z) / -299

Thus, we have the solution for the system of equations in terms of the parameter z:

x = (2046y - 15687) / -5859
y = (-351222 - 63z) / -299
z = z

Comparing this to the expected answer, it appears that there may be a sign error or an error in simplifying the equations in your final solution. Please check your calculations again to ensure accuracy.