Question

Answer two questions about Systems A and B: System A -4х - 6y = 9 3x + y =-4 System B -4x - 6y = 9 -x-5y = 5 How can we get System B from System A?

Answer 1

To get System B from System A, we can manipulate the equations in System A to match the equations in System B. Here's how we can do it step-by-step:

1. Let's start with System A:

-4х - 6y = 9

3x + y = -4

2. In System B, the first equation is the same as in System A, so we don't need to make any changes to it:

-4x - 6y = 9

3. In System B, the second equation is different from System A, so we need to modify the second equation in System A to match it:

-x - 5y = 5

4. To transform the second equation in System A, we can multiply it by (-3) to get rid of the coefficient of "x":

(-3) * (3x + y) = (-3) * (-4)

-9x - 3y = 12

5. Now, we have two equations:

-4x - 6y = 9

-9x - 3y = 12

6. Finally, we can simplify the second equation by dividing it by (-3):

(-9x - 3y) / (-3) = 12 / (-3)

3x + y = -4

7. Now we have System B:

-4x - 6y = 9

3x + y = -4

By following these steps, we were able to transform System A into System B

Answer 2

-4x - 6y = 9 -4x - 6y = 14

Explanation:

To obtain System B from System A, we need to perform certain operations on the equations of System A. Here's how we can do it:

Multiply the second equation of System A by -1 to change the sign of both sides: -1*(3x + y) = -1*(-4) -3x - y = 4

Notice that the first equation of System B is the same as the first equation of System A. However, the second equation of System B is different. We need to obtain this equation.

Add 5 to both sides of the first equation of System A: -4x - 6y + 5 = 9 + 5 -4x - 6y + 5 = 14

Rearrange the terms to match the format of the second equation of System B: -4x - 6y = 14

Now, we have transformed System A into System B by changing the sign of the second equation and adding 5 to the first equation. The resulting system is: -4x - 6y = 9 -4x - 6y = 14

You're welcome! ^^