Question

3x+4y=61 4y+3x=72 Решите систему

Answer 1

В этом поле нужно 20 символов поэтому я это пишу

Answer 2

To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of elimination to find the values of x and y.

Given the system of equations:

1. 3x + 4y = 61
2. 4y + 3x = 72

Step 1: Eliminate one variable by adding the equations.

To eliminate y, we can add equation 1) and equation 2):

(3x + 4y) + (4y + 3x) = 61 + 72 7x + 7y = 133

Step 2: Divide both sides of the equation by 7 to simplify:

x + y = 19

Step 3: Now we have one equation with one variable (x + y = 19). We can use this equation to find the value of y in terms of x:

y = 19 - x

Step 4: Substitute the value of y in terms of x into one of the original equations. Let's use equation 1):

3x + 4(19 - x) = 61

Step 5: Solve for x:

3x + 76 - 4x = 61 -x + 76 = 61 -x = 61 - 76 -x = -15

Step 6: Multiply both sides by -1 to solve for x:

x = 15

Step 7: Now that we have the value of x, we can find the value of y by using the equation we derived in Step 3:

y = 19 - x y = 19 - 15 y = 4

So the solution to the system of equations is x = 15 and y = 4.