Question

Найти решение системы уравнений:{2х2-ху=24 {4х-у=16 Реклама googletag.cmd.push(function() { googletag.display('gpt-ad-brainly_rectangle_in_question'); }); Попроси больше объяснений СледитьОтметить нарушение Женябулгарь2000 03.08.2015 Войти чтобы добавить комментарий googletag.cmd.push(function() { googletag.display('gpt-ad-brainly_rectangle_below-question-first'); }); googletag.cmd.push(function() { googletag.display('gpt-ad-brainly_rectangle_below-question-second'); }); Ответы и объяснения русская25отличник2x²-4x²+16x-24=0-2x²+16x-24=0 |:(-2)x²-8x+12=0D= 64 - 48 = 16x₁= 8+4/2=6x₂=8-4/2 = 2y₁= 4*6-16 = 8y₂= 4*2-16= -8Ответ: (6;8), (2;-8).

Answer 1

To solve the system of equations 2x^2 - xy = 24 and 4x - y = 16, we can use the method of substitution or elimination. Let's use the method of substitution.

Method of Substitution:

1. Solve one equation for one variable in terms of the other variable. - From the second equation, we can solve for y in terms of x: y = 4x - 16.

2. Substitute the expression for the variable found in step 1 into the other equation. - Substitute y = 4x - 16 into the first equation: 2x^2 - x(4x - 16) = 24.

3. Simplify and solve the resulting equation. - Distribute the x: 2x^2 - 4x^2 + 16x = 24. - Combine like terms: -2x^2 + 16x = 24. - Move all terms to one side: -2x^2 + 16x - 24 = 0.

4. Solve the quadratic equation. - To solve the quadratic equation, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a). - In this case, a = -2, b = 16, and c = -24. - Substitute the values into the quadratic formula and solve for x.

Let's calculate the values of x and y using the quadratic formula:

x₁ = (-(16) + √((16)^2 - 4(-2)(-24))) / (2(-2)) x₂ = (-(16) - √((16)^2 - 4(-2)(-24))) / (2(-2))

Calculating the values of x₁ and x₂:

x₁ = (-(16) + √(256 - 192)) / (-4) = (-(16) + √64) / (-4) = (-(16) + 8) / (-4) = -8 / (-4) = 2 x₂ = (-(16) - √(256 - 192)) / (-4) = (-(16) - √64) / (-4) = (-(16) - 8) / (-4) = -24 / (-4) = 6

Now, substitute the values of x into the equation y = 4x - 16 to find the corresponding values of y:

y₁ = 4(2) - 16 = 8 - 16 = -8 y₂ = 4(6) - 16 = 24 - 16 = 8

Therefore, the solution to the system of equations is (x₁, y₁) = (2, -8) and (x₂, y₂) = (6, 8).