Question

Solve the system of equations.

−4x+6y=38
x−5y=−20 (1 point)
Responses

(−5, 3)
left parenthesis negative 5 comma 3 right parenthesis

(35, −3)
left parenthesis 35 comma negative 3 right parenthesis

(5, 3)
left parenthesis 5 comma 3 right parenthesis

(−35, −3)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The correct solution to the system of equations is (5, 3).

Answer 2

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

To solve the system of equations −4x + 6y = 38 and x − 5y = −20, we can use the method of substitution.

Step 1: Solve one equation for one variable. Let's solve the second equation x − 5y = −20 for x:
x = 5y - 20

Step 2: Substitute the expression for x in the first equation:
-4(5y - 20) + 6y = 38

Step 3: Simplify and solve for y:
-20y + 80 + 6y = 38
-14y + 80 = 38
-14y = -42
y = -3

Step 4: Substitute the value of y into the equation x = 5y - 20:
x = 5(-3) - 20
x = -15 - 20
x = -35

Therefore, the solution to the system of equations is (-35, -3).

Answer 3

[AI-generated answer — Explain Bot]

To solve the system of equations:

1. Start by using one of the equations to solve for one variable in terms of the other. Let's solve equation (2) for x:
x - 5y = -20
x = 5y - 20

2. Now substitute this expression for x into the other equation (equation 1) and solve for y:
-4(5y - 20) + 6y = 38
-20y + 80 + 6y = 38
-14y = -42
y = 3

3. Substitute the value of y back into either equation to solve for x. Let's use equation (2):
x - 5(3) = -20
x - 15 = -20
x = -5

Therefore, the solution to the system of equations is (x, y) = (-5, 3).