Question

Решить 4 системы 1. x=2-y 3x-2y=11 2. x-3y=7 -7x+y=-69 3. -2x-7y=-22 4x-6y=4 4. x-3y=15 2x+5y=-3

Answer 1

Ответ:

1). X=3 ;. y = -1

2) x = - 107/10. y = - 59/10

3) x = 4. y = 2

4) x=6. y = -3

Answer 2

To solve the four systems of equations, we'll go through each one step by step. Let's start with the first system:

1. x = 2 - y 3x - 2y = 11

Substitute the value of x from the first equation into the second equation:

3(2 - y) - 2y = 11 6 - 3y - 2y = 11 6 - 5y = 11 -5y = 11 - 6 -5y = 5 y = -1

Now, plug the value of y back into the first equation to find the value of x:

x = 2 - (-1) x = 2 + 1 x = 3

So, the solution to the first system is x = 3 and y = -1.

Next, let's move on to the second system:

2. x - 3y = 7 -7x + y = -69

To eliminate one variable, multiply the first equation by 7 and the second equation by 1:

7x - 21y = 49 -7x + y = -69

Now, add the equations to eliminate x:

(7x - 21y) + (-7x + y) = 49 - 69 -20y = -20 y = 1

Now that we have the value of y, substitute it back into the first equation to find x:

x - 3(1) = 7 x - 3 = 7 x = 7 + 3 x = 10

The solution to the second system is x = 10 and y = 1.

Let's continue with the third system:

3. -2x - 7y = -22 4x - 6y = 4

To eliminate one variable, multiply the first equation by 4 and the second equation by 2:

-8x - 28y = -88 8x - 12y = 8

Add the equations to eliminate x:

(-8x - 28y) + (8x - 12y) = -88 + 8 -40y = -80 y = -80 / -40 y = 2

Now, substitute the value of y back into the first equation to find x:

-2x - 7(2) = -22 -2x - 14 = -22 -2x = -22 + 14 -2x = -8 x = -8 / -2 x = 4

The solution to the third system is x = 4 and y = 2.

Finally, let's solve the fourth system:

4. x - 3y = 15 2x + 5y = -3

To eliminate one variable, multiply the first equation by 2 and the second equation by 1:

2x - 6y = 30 2x + 5y = -3

Subtract the equations to eliminate x:

(2x - 6y) - (2x + 5y) = 30 - (-3) -11y = 33 y = 33 / -11 y = -3

Now, substitute the value of y back into the first equation to find x:

x - 3(-3) = 15 x + 9 = 15 x = 15 - 9 x = 6

The solution to the fourth system is x = 6 and y = -3.

To summarize:

1. x = 3, y = -1
2. x = 10, y = 1
3. x = 4, y = 2
4. x = 6, y = -3