Question

Решить систему методом подстановки x-2y=5 3x+4y=10

Answer 1

{x=5+2y

{3x+4y=10

3*(5+2y)+4y=10

15+6y+4y=10

10-15=10y

10y=-5

y=-0,5

x=5+2*(-0,5)=5-1=4

(4;-0,5)

Answer 2

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

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

Let's apply these steps to the given system:

1. Solve the first equation for x: x - 2y = 5 x = 5 + 2y

2. Substitute the expression for x into the second equation: 3(5 + 2y) + 4y = 10

3. Solve for y: 15 + 6y + 4y = 10 10y + 15 = 10 10y = 10 - 15 10y = -5 y = -5 / 10 y = -1/2

4. Substitute y = -1/2 into the expression for x: x = 5 + 2(-1/2) x = 5 - 1 x = 4

So, the solution to the system of equations is x = 4 and y = -1/2.