Question

[4x-y=13, 2x²-xy=21.

Answer 1

Ответ:(-7,11)(3-1)

Объяснение:

Answer 2

To solve the system of equations:

1. 4x - y = 13
2. 2x² - xy = 21

There are multiple methods to solve this system, such as substitution, elimination, or using matrices. Here, we'll use the substitution method:

From equation 1), we can express y in terms of x: y = 4x - 13

Substitute this value of y into equation 2): 2x² - x(4x - 13) = 21

Simplify: 2x² - 4x² + 13x - 21 = 0

Combine like terms: -2x² + 13x - 21 = 0

To solve this quadratic equation, we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a)

For this equation, a = -2, b = 13, and c = -21.

x = (-(13) ± √((13)² - 4(-2)(-21))) / (2(-2)) x = (-13 ± √(169 - 168)) / (-4) x = (-13 ± √1) / (-4)

x = (-13 ± 1) / (-4)

Solving for x, we have two solutions: x₁ = (-13 + 1) / (-4) = -12 / (-4) = 3 x₂ = (-13 - 1) / (-4) = -14 / (-4) = 7/2 = 3.5

Now, substitute these values of x back into either equation to find the corresponding y-values.

Using equation 1) with x = 3: 4(3) - y = 13 12 - y = 13 -y = 13 - 12 -y = 1 y = -1

So one solution is (x, y) = (3, -1).

Using equation 1) with x = 3.5: 4(3.5) - y = 13 14 - y = 13 -y = 13 - 14 -y = -1 y = 1

So another solution is (x, y) = (3.5, 1).

Therefore, the system of equations has two solutions: (3, -1) and (3.5, 1).