Question

Решить систему 2x-y=4 3x+7y=6

Answer 1

Решение способом сложение:

х=34÷17

х=2

Answer 2

To solve the system of equations:

2x - y = 4 (equation 1) 3x + 7y = 6 (equation 2)

We can use either substitution or elimination method to solve for x and y.

Method 1: Substitution

1. Solve equation 1 for y: y = 2x - 4
2. Substitute y in equation 2 with the expression from step 1: 3x + 7(2x - 4) = 6 3x + 14x - 28 = 6 17x = 34 x = 2
3. Substitute x in equation 1 with the value from step 2 to solve for y: 2(2) - y = 4 y = -2

Therefore, the solution to the system of equations is x = 2 and y = -2.

Method 2: Elimination

1. Multiply equation 1 by 7 to get rid of y in equation 2: 14x - 7y = 28 (equation 1 multiplied by 7) 3x + 7y = 6 (equation 2)
2. Add equation 1 and equation 2: 17x = 34 x = 2
3. Substitute x in equation 1 or equation 2 to solve for y: 2(2) - y = 4 y = -2

Therefore, the solution to the system of equations is x = 2 and y = -2, which is the same as the solution obtained using the substitution method.