Solve the system:

Question

3y - z = -7
2y + z = -4

Answer 1

To solve the system of equations, we can add the two equations together to eliminate the variable "z".

Adding the two equations, we get:
(3y - z) + (2y + z) = (-7) + (-4)
5y = -11

Dividing both sides of the equation by 5, we get:
y = -11/5

Now that we have the value of y, we can substitute it back into one of the original equations to solve for z.

Using the second equation, we have:
2y + z = -4
2(-11/5) + z = -4
-22/5 + z = -4

Adding 22/5 to both sides of the equation, we get:
z = -4 + 22/5
z = -20/5 + 22/5
z = 2/5

So the solution to the system of equations is:
y = -11/5 and z = 2/5.

Answer 2

Can you substitute y into the first equation to solve?

Answer 3

Apologies for the oversight. Yes, we can substitute the value of y into the first equation to solve for z.

From the first equation, 3y - z = -7, substituting the value of y, we have:
3(-11/5) - z = -7
-33/5 - z = -7

Adding 33/5 to both sides of the equation, we get:
-z = -7 + 33/5
-z = -35/5 + 33/5
-z = -2/5

Multiplying both sides of the equation by -1, we get:
z = 2/5

Therefore, the solution to the system of equations is:
y = -11/5 and z = 2/5.