Question

Решение систем уравнений: 3x+2y=-27 -5x+2y=13

Answer 1

Решение систем уравнений:

$\left \{ {{3x+2y=-27} \atop {-5x+2y=13}} \right.$

Вычтем из (1) второе уравнение

$8x = -40 \\ \\ x = -5$

Из второго

$-5*(-5)+2y=13 \\ \\ 2y=38 \\ \\ y = 19$

Ответ: 
$x = -5 \\ \\ y = 19$

Answer 2

To solve the system of equations:

1. 3x + 2y = -27
2. -5x + 2y = 13

We can use the method of elimination. The goal is to eliminate one of the variables (y, in this case) by adding or subtracting the equations. Let's proceed step by step:

Step 1: Multiply both sides of the second equation by 3 to make the coefficients of y in both equations equal:

2a. 3(-5x + 2y) = 3(13) 2b. -15x + 6y = 39

Now, the system becomes:

1. 3x + 2y = -27
2. -15x + 6y = 39

Step 2: Now, let's eliminate y by adding the modified equation 2b to equation 1:

(3x + 2y) + (-15x + 6y) = -27 + 39

Step 3: Simplify the equation:

-12x + 8y = 12

Step 4: Divide the entire equation by 4 to simplify it further:

(-12x + 8y)/4 = 12/4

Step 5: The equation becomes:

-3x + 2y = 3

Step 6: Now we have a new simplified equation. Let's solve for y:

2y = 3 + 3 2y = 6

Step 7: Divide both sides by 2 to find the value of y:

y = 6/2 y = 3

Step 8: Now that we have the value of y, we can substitute it back into either equation 1 or 2 to find the value of x. Let's use equation 1:

3x + 2(3) = -27

Step 9: Simplify the equation:

3x + 6 = -27

Step 10: Move 6 to the other side of the equation:

3x = -27 - 6 3x = -33

Step 11: Finally, divide both sides by 3 to find the value of x:

x = -33/3 x = -11

So, the solution to the system of equations is x = -11 and y = 3.