Question

5х+у=4 х=3+2у решите системы уравнений способом подстановки​

Answer 1

1 способ.

5x+y=4  |×2    10x+2y=8

x=3+2y               x-2y=3

Суммируем эти уравнения:

11x=11  |÷11

x=1   ⇒    

5*1+y=4

5+y=4

y=-1.

Ответ: x=1     y=-1.

2 способ.

5x+y=4

x=3+2y

5*(3+2y)+y=4

15+10y+y=4

11y=-11  |÷11

y=-1

x=3+2*(-1)=3-2=1

Ответ: x=1       y=-1.

Answer 2

To solve the system of equations using the method of substitution, we'll start by solving one equation for one variable and then substitute that expression into the other equation. Let's begin:

Given equations:

1. 5x + y = 4
2. x = 3 + 2y

We'll solve equation 2) for x and substitute it into equation 1).

Substituting equation 2) into equation 1): 5(3 + 2y) + y = 4 15 + 10y + y = 4 11y + 15 = 4 11y = 4 - 15 11y = -11 y = -11 / 11 y = -1

Now, substitute the value of y back into equation 2) to find x: x = 3 + 2(-1) x = 3 - 2 x = 1

Therefore, the solution to the system of equations is x = 1 and y = -1.