Question

Система x+y=4 x^2-y=2

Answer 1

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Готово!!Удачи)))

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Answer 2

х + у = 4 }

х² - у = 2

- - - - - - - - - - - - - - -

х + х² = 4 + 2

х + х² = 6

х = 2

- - - - - - - - - - - - - - -

2 + у = 4

у = 2

Answer 3

To solve the system of equations, we can use the method of substitution or elimination. I'll demonstrate the elimination method here:

Given the system of equations:

1. x + y = 4 ...........(Equation 1)
2. x^2 - y = 2 ........(Equation 2)

Step 1: Solve Equation 1 for y: From Equation 1, we have y = 4 - x.

Step 2: Substitute the value of y from Step 1 into Equation 2: x^2 - (4 - x) = 2

Step 3: Solve for x: x^2 - 4 + x = 2 x^2 + x - 6 = 0

Step 4: Factor the quadratic equation or use the quadratic formula to find the values of x:

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a

In our case, a = 1, b = 1, and c = -6

x = (-(1) ± √((1)^2 - 4(1)(-6))) / 2(1) x = (-1 ± √(1 + 24)) / 2 x = (-1 ± √25) / 2 x = (-1 ± 5) / 2

So, we have two possible values for x:

1. x = ( -1 + 5 ) / 2 = 4 / 2 = 2
2. x = ( -1 - 5 ) / 2 = -6 / 2 = -3

Step 5: Find the corresponding values of y using Equation 1:

For x = 2: y = 4 - x = 4 - 2 = 2

For x = -3: y = 4 - x = 4 - (-3) = 4 + 3 = 7

Step 6: Write the solution: The solution to the system of equations is (x, y) = (2, 2) and (-3, 7).

You can verify these solutions by substituting the values back into both equations.