Question

Реши систему уравнений методом сложения {xa+x=8 xa+a=5 {x1= a1= {x2= a2= Смотреть ответ sardorovna07 sardorovna07 Ответ: Где не понятно спрашивайте

Answer 1

#### Solving the System of Equations by the Method of Addition To solve the system of equations using the method of addition, we need to eliminate one variable by adding the equations together. Let's solve the given system of equations step by step. The given system of equations is: 1. **xa + x = 8** 2. **xa + a = 5** To eliminate the variable "a," we can subtract equation 2 from equation 1. This will result in the elimination of the "a" variable, allowing us to solve for "x." Subtracting equation 2 from equation 1, we get: **(xa + x) - (xa + a) = 8 - 5** Simplifying the equation, we have: **x - a = 3** Now, we have a new equation: 3. **x - a = 3** To solve for "x," we need another equation involving "x" and "a." Let's add equation 1 and equation 2 together to eliminate the variable "xa." Adding equation 1 and equation 2, we get: **(xa + x) + (xa + a) = 8 + 5** Simplifying the equation, we have: **2xa + 2x + a = 13** Now, we have a new equation: 4. **2xa + 2x + a = 13** We now have a system of two equations: 3. **x - a = 3** 4. **2xa + 2x + a = 13** To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution to solve for "x" and "a." From equation 3, we can express "a" in terms of "x" as: **a = x - 3** Substituting this value of "a" into equation 4, we get: **2x(x - 3) + 2x + (x - 3) = 13** Simplifying the equation, we have: **2x^2 - 4x + x - 3 + 2x + x - 3 = 13** **2x^2 - x - 9 = 13** Rearranging the equation, we have: **2x^2 - x - 22 = 0** To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. Let's use the quadratic formula to find the values of "x." The quadratic formula is given by: **x = (-b ± √(b^2 - 4ac)) / (2a)** For our equation, the values of "a," "b," and "c" are: **a = 2** **b = -1** **c = -22** Substituting these values into the quadratic formula, we get: **x = (-(-1) ± √((-1)^2 - 4(2)(-22))) / (2(2))** Simplifying the equation, we have: **x = (1 ± √(1 + 176)) / 4** **x = (1 ± √177) / 4** Therefore, the solutions for "x" are: **x1 = (1 + √177) / 4** **x2 = (1 - √177) / 4** To find the corresponding values of "a," we can substitute these values of "x" into equation 3: **a = x - 3** Substituting the value of "x1" into equation 3, we get: **a1 = (1 + √177) / 4 - 3** Substituting the value of "x2" into equation 3, we get: **a2 = (1 - √177) / 4 - 3** Therefore, the solutions for "a" are: **a1 = (1 + √177) / 4 - 3** **a2 = (1 - √177) / 4 - 3** Please note that the solutions for "x" and "a" are approximate values and may require further simplification or decimal approximation. I hope this helps! Let me know if you have any further questions.