Question

Solve the following system of equations. If there is no solution, write DNE in each coordinate of the ordered triplet. If there are an infinite number of solution, write each coordinate in terms of z

x+3=y+12
z+13=x+8
y-7=z-11
PLS

Answer 1

The solution to the system of equations is (y, x, z) = (22, 9, 18).

Here's how to solve the system of equations:

From the first equation, we can see that y = x - 3 + 12 = x + 9.

Substituting this expression for y into the third equation, we get:

x + 9 - 7 = z - 11

x + 2 = z

Substituting this expression for z into the second equation, we get:

x + 21 = x + 8 + 13

x + 21 = x + 21

This equation is true for all values of x, which means there are an infinite number of solutions. However, we can still find a specific solution by using any of the equations we've derived so far.

Using the expression for y in terms of x, we get:

y = x + 9

Using the expression for z in terms of x, we get:

z = x + 2

We can now substitute these expressions for y and z into any of the original equations to solve for x. Using the second equation, we get:

x + 13 = x + 8 + 13

x = 9

Now that we know x, we can substitute it into the expressions for y and z to get:

y = x + 9 = 18

z = x + 2 = 11

Therefore, the solution to the system of equations is (y, x, z) = (22, 9, 18).

Answer 2

In the photo in which I solved this, it shows that z is 2. Hope this helps :)