Question

Дана система уравнений {ax−3y=36 5x+by=29 Известно, что пара чисел (3; 4) является её решением. Найди значения a и b. Смотреть ответ PontiacBonneville PontiacBonneville Ответ: а=16 b=3,5 Объяснение: нужно объяснение? можно объяснение? хотел бы понять принцип, заранее спасибо

Answer 1

System of Equations

The given system of equations is:

ax - 3y = 36
5x + by = 29

We are told that the pair of numbers (3, 4) is a solution to this system of equations. We need to find the values of `a` and `b`.

Solution

To find the values of `a` and `b`, we can substitute the given solution (3, 4) into the system of equations and solve for `a` and `b`.

Substituting x = 3 and y = 4 into the first equation:

a(3) - 3(4) = 36
3a - 12 = 36
3a = 48
a = 16

Substituting x = 3 and y = 4 into the second equation:

5(3) + b(4) = 29
15 + 4b = 29
4b = 14
b = 3.5

Therefore, the values of `a` and `b` are:

a = 16
b = 3.5

Explanation:

To find the values of `a` and `b`, we substitute the given solution (3, 4) into the system of equations and solve for `a` and `b`. This is done by substituting the values of x and y into each equation and simplifying the resulting expressions.

In the first equation, substituting x = 3 and y = 4 gives us:

a(3) - 3(4) = 36
3a - 12 = 36
3a = 48
a = 16

In the second equation, substituting x = 3 and y = 4 gives us:

5(3) + b(4) = 29
15 + 4b = 29
4b = 14
b = 3.5

Therefore, the values of `a` and `b` are:

a = 16
b = 3.5

I hope this explanation helps! Let me know if you have any further questions.