Question

X – Зу = 5,3х – 9y = 15;​

Answer 1

Если первое уравнение умножить на 3, то получим второе уравнение, значит, прямые сольются, и и система поэтому будет иметь бесконечно много решений. например, если выразить х через у из первого уравнения.  х=5+3у, то получим при подстановке любого у значения для х, например, если у=0, то х=5, (5;0) - одно из решений системы. аналогично можно получить и другие.

Answer 2

To solve this system of linear equations for the variables x and y, you can use the method of substitution or elimination. I'll use the elimination method here:

The given system of equations is:

1. X - 2y = 5
2. 3x - 9y = 15

First, let's simplify the second equation by dividing both sides by 3 to make it easier to work with:

2. (1/3)(3x - 9y) = (1/3)(15)
3. x - 3y = 5

Now, we have the system of equations:

1. X - 2y = 5
2. x - 3y = 5

We can eliminate y by multiplying the first equation by 3 and the second equation by 2 so that the coefficients of y in both equations will cancel each other out:

1. (3)(X - 2y) = (3)(5)
2. (2)(x - 3y) = (2)(5)

This gives us:

4. 3x - 6y = 15
5. 2x - 6y = 10

Now, subtract equation 5 from equation 4 to eliminate y:

(3x - 6y) - (2x - 6y) = 15 - 10

Simplify:

x = 5

Now that we have the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use equation 1:

X - 2y = 5

Substitute x = 5:

5 - 2y = 5

Now, isolate y:

-2y = 5 - 5 -2y = 0

Divide by -2:

y = 0

So, the solution to the system of equations is x = 5 and y = 0.