Question

How many solution(s) does the system of equations have? −5x+y=−18 10x−2y=36 (1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The system of equations has exactly one solution.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To determine the number of solutions, we can use the concept of slopes in linear equations.

The given system of equations is:
-5x + y = -18 ---(1)
10x - 2y = 36 ---(2)

By rearranging equation (1), we have:
y = 5x - 18.

We can see that the coefficient of x in equation (1) is positive, which indicates a positive slope.

Similarly, by rearranging equation (2), we have:
y = 5x - 18.

We can see that the coefficient of x in equation (2) is also positive, which indicates a positive slope.

Since the slopes of the two equations are equal, the two lines will be parallel.

When two lines are parallel, they do not intersect and there are no common solutions.

Therefore, the given system of equations has no solution or is inconsistent.

Answer 3

[AI-generated answer — Explain Bot]

To determine the number of solutions for the given system of equations, we can solve the equations and analyze the solution.

Let's start by solving the system of equations:

Equation 1: -5x + y = -18
Equation 2: 10x - 2y = 36

To solve the system, we can use any method such as substitution, elimination, or graphing. Here, we will use the substitution method.

Step 1: Solve Equation 1 for y.
-5x + y = -18
y = -18 + 5x

Step 2: Substitute the value of y in Equation 2.
10x - 2(-18 + 5x) = 36

Simplify and solve:
10x + 36 - 10x = 36
36 = 36

Step 3: Analyze the result.
The equation 36 = 36 is a true statement. This means that the two equations are identical and have infinitely many solutions.

Therefore, the system of equations has infinitely many solutions.