Question

how many solutions does this equation have?

-5x+y=-18
10x-2y=36

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine the number of solutions for a system of equations, we need to solve the equations and see if they intersect at one point (one solution), are parallel (no solution), or overlap (infinitely many solutions).

Rearranging the first equation, we have:

y = 5x - 18

Substitute this value of y into the second equation:

10x - 2(5x - 18) = 36
10x - 10x + 36 = 36
36 = 36

As a result, this means that the second equation is satisfied by any value of x. Therefore, the system of equations has infinitely many solutions.

Answer 2

[AI-generated answer — Explain Bot]

To find the number of solutions for this system of equations, we need to solve the equations and observe the relationship between the variables.

Let's solve the system of equations using the method of substitution:

Step 1: Solve the first equation for y:
-5x + y = -18
y = 5x - 18

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

Step 3: Simplify and analyze the result:
The equation 36 = 36 is a true statement, meaning that both equations are equivalent. As a result, we have infinitely many solutions.

In conclusion, the given system of equations has infinitely many solutions.

Answer 3

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

To find the number of solutions for this system of equations, we can use the method of solving them simultaneously.

We have the following system of equations:

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

We can use either the substitution method or the elimination method to solve this system.

Let's solve it using the elimination method:

Step 1: Multiply Equation 1 by 2 to make the coefficients of y in both equations equal:

2 * (-5x + y) = 2 * (-18)
-10x + 2y = -36

Now we have the following system:

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

Step 2: Add the two equations together to eliminate the variable y:

(-10x + 2y) + (10x - 2y) = -36 + 36
-10x + 10x + 2y - 2y = 0
0 = 0

Step 3: Since the equation 0 = 0 holds true, it implies that the two equations are equivalent. This means that the two equations represent the same line and therefore have infinitely many solutions.

Therefore, the given system of equations has infinitely many solutions.