Question

Решите систему 6x+y=10 6x-3y=-26​

Answer 1

6х+у=10

6х-3у=-26 I*(-1)

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6х+у=10

-6х+3у=26  сложим

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4у=36; у=9

6х+9=10; 6х=1; х=1/6

Ответ: (1/6; 9)

Answer 2

Ответ:

\left \{ {{6x+y=10} \atop {6x-3y=-26}} \right.  =  \left \{ {{y=10-6x} \atop {6x-3y=-26}} \right.  = 6x-3(10-6x) = -26

6x-30+18x=-26

24x=-26+30

24x=4

x= \frac{1}{6}  

y = 10- \frac{1}{6}  = 9

Answer 3

To solve the system of equations, we can use the method of elimination or substitution. Let's use the elimination method in this case.

Given the system of equations:

1. 6x + y = 10
2. 6x - 3y = -26

Step 1: Multiply both sides of equation 1 by 3 to make the coefficients of y in both equations equal:

3 * (6x + y) = 3 * 10 18x + 3y = 30

Step 2: Now, add equation 2 to the modified equation from step 1:

(18x + 3y) + (6x - 3y) = 30 - 26

Step 3: Simplify the equation:

24x = 4

Step 4: Solve for x:

x = 4 / 24 x = 1/6

Step 5: Substitute the value of x back into either equation 1 or 2 to solve for y. Let's use equation 1:

6x + y = 10 6 * (1/6) + y = 10 1 + y = 10

Step 6: Solve for y:

y = 10 - 1 y = 9

So the solution to the system of equations is x = 1/6 and y = 9.