Question

Имеет ли решения система -3х+2у=7 6х-4у=7 и сколько? Помогите пожалуйста

Answer 1

Solution to the System of Equations

To find the solutions to the system of equations -3x + 2y = 7 and 6x - 4y = 7, we can use the method of substitution or elimination. Let's solve it using the elimination method.

To eliminate one variable, we can multiply the first equation by 2 and the second equation by 3. This will allow us to eliminate the y variable when we add the two equations together.

Multiplying the first equation by 2, we get:

-6x + 4y = 14 Multiplying the second equation by 3, we get:

18x - 12y = 21 Now, we can add the two equations together:

(-6x + 4y) + (18x - 12y) = 14 + 21

Simplifying the equation, we have:

12x - 8y + 18x - 12y = 35

Combining like terms, we get:

30x - 20y = 35

Dividing both sides of the equation by 5, we have:

6x - 4y = 7 We can see that this equation is the same as the first equation in the original system. This means that the two equations represent the same line and have infinitely many solutions. Any point on the line -3x + 2y = 7 will satisfy both equations.

Therefore, the system of equations has infinitely many solutions.

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