Question

Решите систему методом подставки: 4y-x=11 5x-2y= 17

Answer 1

4y - x = 11
5x - 2y = 17

4y - 11 = x
5x - 2y = 17

x = 4y - 11
5(4y - 11) - 2y = 17

20y - 55 - 2y = 17
18y = 72
y = 4

x = 4*4 - 11
x = 5

x = 5
y = 4

Answer 2

To solve the system of equations using the method of substitution, we'll follow these steps:

Step 1: Solve one of the equations for one variable in terms of the other variable. Step 2: Substitute the expression obtained in Step 1 into the other equation. Step 3: Solve the resulting equation for the variable found in Step 1. Step 4: Substitute the value of the variable found in Step 3 back into any of the original equations to find the value of the other variable.

Let's start with the given system of equations:

1. 4y - x = 11
2. 5x - 2y = 17

Step 1: Solve equation (1) for x in terms of y: x = 4y - 11

Step 2: Substitute the expression x = 4y - 11 into equation (2): 5(4y - 11) - 2y = 17

Step 3: Solve for y: 20y - 55 - 2y = 17 18y - 55 = 17 18y = 17 + 55 18y = 72 y = 72 / 18 y = 4

Step 4: Now that we have the value of y, we can find the value of x by substituting y back into equation (1): x = 4(4) - 11 x = 16 - 11 x = 5

So the solution to the system of equations is x = 5 and y = 4.