Question

3x + 2y=8 6x - 14y =6 решите систему уравнений

Answer 1

{3х+2у=8 |*(-2)
{6х-14у=6

{-6х-4у=-16
{6х-14у=6
___________
-18у=-10
у= 10/18=5/9

$6x - \frac{14}{1} \times \frac{5}{9} = 6 \\ 6x - \frac{70}{9} = 6 \\ 6x = 13 \frac{7}{9} \\ x = \frac{124}{9} \times \frac{1}{6} \\ x = \frac{62}{27} \\ x = 2 \frac{8}{27} \: \:$


Ответ: (2 8/27; 5/9)

Answer 2

To solve the system of equations, we can use either the substitution method or the elimination method. I'll use the elimination method in this case.

Given the system of equations:

1. 3x + 2y = 8
2. 6x - 14y = 6

Step 1: Multiply the first equation by 7 to eliminate the y variable. (7) * (3x + 2y) = (7) * 8 21x + 14y = 56

Step 2: Add the modified first equation to the second equation to eliminate the y variable. (21x + 14y) + (6x - 14y) = 56 + 6 27x = 62

Step 3: Solve for x. x = 62 / 27 ≈ 2.2963 (rounded to 4 decimal places)

Step 4: Substitute the value of x back into either of the original equations to find y. Let's use the first equation. 3x + 2y = 8 3 * 2.2963 + 2y = 8 6.8889 + 2y = 8 2y = 8 - 6.8889 2y = 1.1111

Step 5: Solve for y. y = 1.1111 / 2 ≈ 0.5556 (rounded to 4 decimal places)

So, the solution to the system of equations is approximately: x ≈ 2.2963 y ≈ 0.5556