Question

Solve the system of two linear equations.

−3x−4y=−23
3x−5y=5 (1 point)
Responses

(5, 2)
left parenthesis 5 comma 2 right parenthesis

(5,−2)
left parenthesis 5 comma negative 2 right parenthesis

(−5,−2)
left parenthesis negative 5 comma negative 2 right parenthesis

(−5, 2)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the system of two linear equations, we can use the method of elimination. Adding the two equations together eliminates the x-term:

(-3x - 4y) + (3x - 5y) = -23 + 5
-3x + 3x - 4y - 5y = -18
-9y = -18

Dividing both sides by -9:
y = 2

Substituting this value of y into one of the original equations, we can solve for x:

-3x - 4(2) = -23
-3x - 8 = -23
-3x = -15
x = 5

Therefore, the solution to the system of equations is (5, 2).

Answer 2

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

To solve the system of equations −3x−4y=−23 and 3x−5y=5:

Step 1: Multiply the first equation by 3 and the second equation by -3 to eliminate x:
-9x - 12y = -69
-9x + 15y = -15

Step 2: Add the two resulting equations together to eliminate x:
(-9x - 12y) + (-9x + 15y) = -69 + (-15)
-18y = -84

Step 3: Divide both sides of the equation by -18 to solve for y:
y = -84 / -18
y = 4.67 (rounded to two decimal places)

Step 4: Substitute the value of y back into one of the original equations, for example, the second equation:
3x - 5 * 4.67 = 5

Step 5: Simplify and solve for x:
3x - 23.35 = 5
3x = 28.35
x = 9.45 (rounded to two decimal places)

So the solution to the system of equations is (9.45, 4.67).

Answer 3

[AI-generated answer — Explain Bot]

To solve this system of equations, we can use the elimination or substitution method. Let's use the elimination method:

First, let's rearrange the second equation to make the x-coefficient the same as the first equation:

3x - 5y = 5

Multiply both sides of the second equation by -1:

-3x + 5y = -5

Now, we can add the two equations:

(-3x - 4y) + (-3x + 5y) = (-23) + (-5)

Simplifying:

-6x + y = -28

Now we have a new equation. Let's call it equation (3).

Next, we'll solve equations (1) and (3) as a system of equations. We'll multiply both sides of equation (1) by 6 to make the x-coefficient in both equations the same:

-18x - 24y = -138

Now we have two equations:

-18x - 24y = -138 (equation 4)
-6x + y = -28 (equation 3)

To eliminate the y variable, we'll multiply equation (3) by 24, and equation (4) by -1:

-24(-6x + y) = -24(-28) becomes 144x - 24y = 672 (equation 5)

x is eliminated in equation (4):

18x + 24y = 138 (equation 6)

Now, let's add equations (5) and (6):

(144x - 24y) + (18x + 24y) = 672 + 138

Simplifying:

162x = 810

Divide both sides by 162:

x = 5

Now, substitute the value of x into equation (3):

-6(5) + y = -28

Simplifying:

-30 + y = -28

Add 30 to both sides:

y = -28 + 30

Simplifying:

y = 2

Therefore, the solution to the system of equations is (x, y) = (5, 2).