Вопрос
Bapsaur 76 (2024 r.) 1) ) x_(1)-2x_(2)+2x_(3)-4x_(4)=-2 -5x_(1)+8x_(2)-4x_(3)+12x_(4)=-4 x_(1)-7x_(2)+5x_(3)-12x_(4)=-1 -2x_ 2) ) x_(1)+x_(2)+2x_(3)=1 2x_(1)-x_(2)+2x_(3)=-4 4x_(1)+x_(2)+4x_(3)=-2
Решения
4.7
(282 Голоса)
Венера
ветеран · Репетитор 9 лет
Ответ
1) To solve the system of equations, we can use the method of substitution or elimination. Let's use the elimination method.First, let's multiply the first equation by 2 and the second equation by 1 to make the coefficients of
in both equations equal:
Now, let's add the two equations:
Simplifying the equation:
Now, let's multiply the third equation by 1 and the fourth equation by 2 to make the coefficients of
in both equations equal:
Now, let's add the two equations:
Simplifying the equation:
Now we have two new equations:
We can solve this system of equations using the elimination method again. Let's multiply the second equation by 3 to make the coefficients of
in both equations equal:
Now, let's subtract the second equation from the first:
Simplifying the equation:
Now we have a new equation:
We can solve this equation using the substitution method. Let's solve for
:
Now, let's substitute this value of
into the first equation:
Simplifying the equation:
Multiplying through by 13 to clear the fraction:
Combining like terms:
Now, let's solve for
:
Now, let's substitute this value of
into the equation for
:
Simplifying the equation:$x_{2}=\frac{1+\frac{1836+1428x_{4}}{65