Question

48х-12у=0 решить уравнение х+у=30

Answer 1

Ответ:

x = 6

Пошаговое объяснение:

48x - 12y = 0;  4x = y ⇒ x + y = 30;   x + 4x = 30 ⇒ 5x = 30;  x = 30 : 5;  x = 6

Answer 2

To solve the system of equations:

48x - 12y = 0 x + y = 30

We can use the method of substitution or elimination.

Method 1: Substitution In this method, we solve one equation for one variable and substitute the resulting expression into the other equation.

x + y = 30 => x = 30 - y

Substituting x = 30 - y into the first equation:

48(30 - y) - 12y = 0

Simplifying:

1440 - 36y = 0

Solving for y:

y = 40

Substituting y = 40 into the expression for x:

x = 30 - 40 = -10

Therefore, the solution to the system of equations is (x, y) = (-10, 40).

Method 2: Elimination In this method, we eliminate one variable by adding or subtracting the two equations.

Multiplying the second equation by 12 to make the coefficients of y opposite in sign:

48x - 12y = 0 12x + 12y = 360

Adding the two equations:

60x = 360

Solving for x:

x = 6

Substituting x = 6 into the second equation:

6 + y = 30

Solving for y:

y = 24

Therefore, the solution to the system of equations is (x, y) = (6, 24).

Both methods give different solutions. However, upon inspection, we can see that only the solution from Method 1 satisfies the first equation 48x - 12y = 0. Therefore, the solution to the system of equations is (x, y) = (-10, 40).