Question

3x+5y=1. 4x+3y=-6 решить систему

Answer 1

Выразим у из первого уравнения.
5у=1-3х; у=(1-3х)/5
Подставим во второе уравнение.
4х+3((1-3х)/5)=-6
Посчитаешь сам дольше. Чему равен х будет. Подставишь в первое уравнение вместо х и найдёшь у.

Answer 2

To solve the system of equations, we can use either the substitution method, elimination method, or matrix method. I'll demonstrate the elimination method here:

Given the system of equations:

1. 3x + 5y = 1
2. 4x + 3y = -6

Step 1: Multiply both equations to create a common coefficient for either x or y that will allow us to eliminate one of the variables. Let's make the coefficients of y in both equations the same, so we can eliminate y.

Multiply equation (1) by 3 and equation (2) by 5: 3 * (3x + 5y) = 3 * 1 5 * (4x + 3y) = 5 * (-6)

Simplify:

1. 9x + 15y = 3
2. 20x + 15y = -30

Step 2: Now, subtract equation (1) from equation (2) to eliminate y. (20x + 15y) - (9x + 15y) = -30 - 3

Simplify: 11x = -33

Step 3: Solve for x: x = -33 / 11 x = -3

Step 4: Substitute the value of x back into either equation (1) or (2) to solve for y. I'll use equation (1): 3x + 5y = 1 3(-3) + 5y = 1 -9 + 5y = 1

Step 5: Solve for y: 5y = 1 + 9 5y = 10 y = 10 / 5 y = 2

So, the solution to the system of equations is x = -3 and y = 2.