Question

Solve the system. 3a+4b=9; -3a-2b=-3

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations, we can use the method of elimination. By adding the two equations together, we can eliminate the variable a:

(3a + 4b) + (-3a - 2b) = 9 + (-3)
3a - 3a + 4b - 2b = 6
2b = 6
b = 3

Now that we have the value of b, we can substitute it back into one of the original equations to find the value of a:

3a + 4(3) = 9
3a + 12 = 9
3a = 9 - 12
3a = -3
a = -1

Therefore, the solution to the system of equations is a = -1, b = 3.

Answer 2

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

To solve the system of equations:

First, we will eliminate one variable to find the value of the other variable. In this case, we can eliminate the 'a' variable by adding the two equations together. When we add the equations, the 'a' terms will cancel out:

(3a + 4b) + (-3a - 2b) = 9 + (-3)

Simplifying, we have:

3a - 3a + 4b - 2b = 9 - 3

This reduces to:

2b = 6

Now, we will solve for 'b' by dividing both sides of the equation by 2:

b = 6/2

b = 3

Now that we have the value of 'b', we can substitute it back into one of the original equations to solve for 'a'. Let's use the first equation:

3a + 4(3) = 9

Simplifying, we have:

3a + 12 = 9

Next, we will isolate the 'a' variable by subtracting 12 from both sides:

3a = 9 - 12

3a = -3

Finally, we will solve for 'a' by dividing both sides of the equation by 3:

a = -3/3

a = -1

Therefore, the solution to the system of equations is a = -1 and b = 3.