Question

2)x - y = 7,( x + y = 23;3)x + y = 32,x - y =14;​

Answer 1

Ответ:

2. х = 15;  у = 8

3. х = 23;  у = 9

Пошаговое объяснение:

Решение методом подстановки:

2) x - y = 7

x + y = 23

Из 1-го уравнения:

у = х-7 → подставим значение у во 2-е уравнение:

х+х-7 = 23

2х = 30

х = 30/2

х = 15 → подставим значение х в первое уравнение:

15-у = 7

у = 15-7

у = 8

3) x + y = 32

x - y = 14

Из 1-го уравнения:

у = 32-х → подставим значение у во 2-е уравнение:

х - 32 + х = 14

2х = 46

х = 46/2

х = 23 → подставим значение х в первое уравнение:

23 + у = 32

у = 32 - 23

у = 9

Решение методом сложения:

2) x - y = 7 → сложим отдельно обе части уравнения:

x + y = 23

х-у+х+у = 7+23

2х = 30

х = 30/2

х = 15 → подставим значение х во 2-е уравнение:

15 + у = 23

у = 23-15

у = 8

3) x + y = 32 → сложим отдельно обе части уравнения:

x - y =14

х+у+х-у = 46

2х = 46

х = 46/2

х = 23 → подставим значение х во 2-е уравнение:

23 - у = 14

у = 23-14

у = 9

Answer 2

To solve these systems of linear equations, you can use the method of elimination. I'll show you how to solve each system:

1. x - y = 7 x + y = 23

Add the two equations together to eliminate the variable y:

(x - y) + (x + y) = 7 + 23 2x = 30

Now, divide both sides by 2 to isolate x:

2x/2 = 30/2 x = 15

Now that you have the value of x, you can substitute it back into one of the original equations to solve for y. Let's use the first equation:

x - y = 7 15 - y = 7

Subtract 15 from both sides:

-y = 7 - 15 -y = -8

Now, multiply both sides by -1 to solve for y:

y = 8

So the solution to the first system is x = 15 and y = 8.

2. x + y = 32 x - y = 14

Add the two equations together to eliminate the variable y:

(x + y) + (x - y) = 32 + 14 2x = 46

Now, divide both sides by 2 to isolate x:

2x/2 = 46/2 x = 23

Now that you have the value of x, you can substitute it back into one of the original equations to solve for y. Let's use the first equation:

x + y = 32 23 + y = 32

Subtract 23 from both sides:

y = 32 - 23 y = 9

So the solution to the second system is x = 23 and y = 9.