The system has infinitely many solutions. The solution set is given by
y = 9 + 4t and z = t , where t can be any real number.
Let's solve the system of equations step by step:
Given system of equations:
1. 5y - 20z = 45
2. y - 4z = 9
We can start by solving one of the equations for one variable and then substitute it into the other equation. Let's solve the second equation for y:
Equation 2:
y - 4z = 9
Add 4z to both sides:
y = 9 + 4z
Now, substitute this expression for y into the first equation:
Equation 1:
5y - 20z = 45
Substitute 9 + 4z for y:
5(9 + 4z) - 20z = 45
Distribute the 5:
45 + 20z - 20z = 45
Combine like terms:
45 = 45
This equation is true, which means that any value of z will satisfy it. Let's denote z as a parameter t. Now, substitute z = t back into
y = 9 + 4z:
y = 9 + 4t
So, the solution to the system is y = 9 + 4t and z = t, where t can be any real number. This represents an infinite number of solutions, indicating that the system is dependent and has infinitely many solutions.