Question

2x+4y=6 x-y=13 решить систему

Answer 1

X=13+y
2(13+y)+4y=16
26+2y+4y=16
6y=-10
y=-10/6=-5/3
x=13-5/3=11 2/3
Ответ: (11 2/3; -5/3)

Answer 2

To solve the system of equations:

1. 2x + 4y = 6
2. x - y = 13

We can use either the substitution method or the elimination method. Let's use the elimination method:

Step 1: Multiply the second equation by 4 to make the coefficients of y in both equations equal:

2 * (x - y) = 2 * 13 2x - 2y = 26

Step 2: Now, we have the following system of equations:

1. 2x + 4y = 6
2. 2x - 2y = 26

Step 3: Subtract the second equation from the first equation to eliminate x:

(2x + 4y) - (2x - 2y) = 6 - 26 2x + 4y - 2x + 2y = -20 6y = -20

Step 4: Solve for y:

y = -20 / 6 y = -10 / 3

Step 5: Now that we have the value of y, we can substitute it back into either of the original equations to solve for x. Let's use the second equation:

x - (-10 / 3) = 13 x + 10 / 3 = 13

Step 6: Solve for x:

x = 13 - 10 / 3 x = (39 - 10) / 3 x = 29 / 3

So, the solution to the system of equations is x = 29/3 and y = -10/3.