Question

{2a+3b=3 {2a-3b=9. Это система Решите пж Посмотреть ответы nadia2690 nadia2690 Думаю це правильно на 100% globys36 globys36 Вот решение по действиям. Надеюсь вы делаете так же

Answer 1

Solving the System of Equations

To solve the system of equations 2a + 3b = 3 and 2a - 3b = 9, we can use the method of elimination or substitution. Let's solve it using the elimination method.

1. Multiply the first equation by 2 and the second equation by 3 to eliminate the variable 'a': - Equation 1: 4a + 6b = 6 - Equation 2: 6a - 9b = 27

2. Subtract the second equation from the first equation to eliminate 'a': - (4a + 6b) - (6a - 9b) = 6 - 27 - Simplifying, we get: -2a + 15b = -21

3. Now we have a new equation: -2a + 15b = -21.

4. Next, we can solve this new equation simultaneously with one of the original equations. Let's use the first equation, 2a + 3b = 3.

5. Multiply the first equation by 2 to make the coefficients of 'a' in both equations the same: - Equation 1: 4a + 6b = 6 - Equation 3: -4a - 6b = -6

6. Add the first equation and the third equation to eliminate 'a': - (4a + 6b) + (-4a - 6b) = 6 - 6 - Simplifying, we get: 0 + 0 = 0

7. The equation 0 = 0 indicates that the two equations are dependent, meaning they represent the same line. This means that the system of equations has infinitely many solutions.

8. Therefore, any values of 'a' and 'b' that satisfy one of the equations will also satisfy the other equation. We can choose any value for 'a' or 'b' and find the corresponding value for the other variable.

For example, let's choose 'a' as a free variable and solve for 'b' using the first equation:

- Let 'a' = 0: - Substitute 'a' = 0 into the first equation: 2(0) + 3b = 3 - Simplifying, we get: 3b = 3 - Solving for 'b', we find: b = 1

So, one possible solution to the system of equations is a = 0 and b = 1.

Note: This is just one possible solution, and there are infinitely many other solutions to the system of equations.

I hope this helps! Let me know if you have any further questions.