Question

Решите систему 4х-3y=-14 -3x2+3y=-18

Answer 1

Метод алгебраического сложения

Answer 2

To solve the system of equations:

1. 4x - 3y = -14
2. -3x^2 + 3y = -18

We can use the method of substitution or elimination. Let's use the substitution method:

Step 1: Solve one equation for one variable in terms of the other variable.

Let's solve equation (1) for y:

1. 4x - 3y = -14

Rearrange the equation to isolate y:

3y = 4x + 14

Now, divide both sides by 3:

y = (4x + 14) / 3

Step 2: Substitute the expression for y from equation (1) into equation (2).

2. -3x^2 + 3y = -18

Substitute (4x + 14) / 3 for y:

-3x^2 + 3((4x + 14) / 3) = -18

Step 3: Simplify and solve for x:

-3x^2 + 4x + 14 = -18

Now, bring everything to one side of the equation:

-3x^2 + 4x + 14 + 18 = 0

Combine like terms:

-3x^2 + 4x + 32 = 0

Step 4: To solve this quadratic equation, we can use the quadratic formula:

The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / 2a

where a = -3, b = 4, and c = 32.

x = (-(4) ± √(4^2 - 4(-3)(32))) / 2(-3)

x = (-4 ± √(16 + 384)) / (-6)

x = (-4 ± √400) / (-6)

x = (-4 ± 20) / (-6)

Now, calculate two possible values of x:

1. x = (20 - 4) / (-6) = 16 / (-6) = -8/3
2. x = (-20 - 4) / (-6) = -24 / (-6) = 4

Step 5: Now that we have two values of x, we can find the corresponding values of y using equation (1):

For x = -8/3: y = (4x + 14) / 3 y = (4(-8/3) + 14) / 3 y = (-32/3 + 14) / 3 y = (-32/3 + 42/3) / 3 y = (10/3) / 3 y = 10/9

For x = 4: y = (4x + 14) / 3 y = (4(4) + 14) / 3 y = (16 + 14) / 3 y = 30 / 3 y = 10

So the solutions to the system of equations are (x = -8/3, y = 10/9) and (x = 4, y = 10).