Question

How many solution does 5y-20z=45 y-4z=9

Answer 1

There are infinitely many solutions for the system of equations.

Step-by-step explanation:

To find the number of solutions for the system of equations:

5y - 20z = 45

y - 4z = 9

We can use the method of substitution. Rearrange the second equation to solve for y:

y = 4z + 9

Substitute this expression for y in the first equation:

5(4z + 9) - 20z = 45

Simplify and solve for z:

20z + 45 - 20z = 45

45 = 45

Since the equation is true, this means that z can be any value. Therefore, there are infinitely many solutions for this system of equations.

Answer 2

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.