Question

Solve for the system equation

-7x-2y=-13
x-2y=11

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations, we can use the method of substitution.

First, we can solve the second equation for x in terms of y:
x - 2y = 11
x = 2y + 11

Now, substitute this expression for x in the first equation:
-7(2y + 11) - 2y = -13
-14y - 77 - 2y = -13
-16y - 77 = -13
-16y = 64
y = -4

Now, substitute this value of y in the first equation to solve for x:
-7x - 2(-4) = -13
-7x + 8 = -13
-7x = -21
x = 3

Therefore, the solution to the system of equations is x = 3 and y = -4.

Answer 2

[AI-generated answer — Explain Bot]

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

We have two equations:

Equation 1: -7x - 2y = -13
Equation 2: x - 2y = 11

From Equation 2, we can isolate x:

x = 2y + 11

Now, substitute this expression for x in Equation 1:

-7(2y + 11) - 2y = -13

Simplify the equation:

-14y - 77 - 2y = -13
-16y - 77 = -13
-16y = 64
y = -4

Now that we have the value of y, substitute it back into Equation 2 to find x:

x - 2(-4) = 11
x + 8 = 11
x = 3

Therefore, the solution to the system of equations is x = 3 and y = -4.

Answer 3

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

To solve the system of equations:

1. We can either use the substitution method or the elimination method. Here, we'll use the elimination method.
2. Multiply the second equation by -7 to make the coefficients of the y-terms equal.

-7(x - 2y) = -7(11)
-7x + 14y = -77

3. Now we have the system of equations:
-7x - 2y = -13
-7x + 14y = -77

4. Add the two equations together to eliminate the x-term:
(-7x -2y) + (-7x + 14y) = -13 + (-77)
-14y = -90

5. Divide both sides by -14:
y = -90 / -14
y = 45/7

6. Substitute this value of y into either of the original equations (let's use the second equation):

x - 2(45/7) = 11

7. Simplify the equation by multiplying through by 7 to get rid of the fraction:

7x - 90 = 77

8. Add 90 to both sides:

7x = 167

9. Divide both sides by 7:

x = 167 / 7
x = 23.8571 (rounded to 4 decimal places)

Thus, the solution to the system of equations is:
x = 23.8571 and y = 45/7.