Question

А)х+у=7 2х+у=8 Б)х-2у=5 х-3у=6

Answer 1

А)
$x + y = 7 \\ 2x + y = 8$
Из второго уравнения вычтем первое:
$x = 1 \\ y = 7 - x \\ \\ x = 1 \\ y = 7 - 1 = 6$
Ответ: (1; 6)

б)
$x - 2y = 5 \\ x - 3y = 6$
Из первого уравнения вычтем второе:
$y = - 1 \\ x = 5 + 2y \\ \\ y = - 1 \\ x = 5 + 2 \times ( - 1) = 5 - 2 = 3$
Ответ: (3; -1)

Answer 2

To solve the system of equations, we can use the method of substitution or elimination. Let's solve it using the method of substitution.

System of Equations A:

1. x + y = 7
2. 2x + y = 8

From equation 1, we can express x in terms of y: x = 7 - y

Substitute this value of x into equation 2: 2(7 - y) + y = 8 14 - 2y + y = 8 -y = 8 - 14 -y = -6 y = 6

Now substitute the value of y back into equation 1 to find x: x + 6 = 7 x = 7 - 6 x = 1

So, the solution to System A is x = 1 and y = 6.

System of Equations B:

1. x - 2y = 5
2. x - 3y = 6

From equation 1, we can express x in terms of y: x = 5 + 2y

Substitute this value of x into equation 2: (5 + 2y) - 3y = 6 5 - y = 6 -y = 6 - 5 -y = 1 y = -1

Now substitute the value of y back into equation 1 to find x: x - 2(-1) = 5 x + 2 = 5 x = 5 - 2 x = 3

So, the solution to System B is x = 3 and y = -1.

Therefore, the solutions to the systems of equations are: System A: x = 1 and y = 6 System B: x = 3 and y = -1