Question

Решите систему уравнений методом сложения 3 х+2 у=3 2 х+5 у=13 и 2 х-3 у=5 3 х+2 у=14 ПОЖАЛУЙСТА ❤

Answer 1

3 х+2 у=3
2 х+5 у=13

6x+4y=6
6x+15y=39

6x+4y-6x-15y= -33
-11y= -33
y= 3

3x+2×3=3
3x= -3
x= -1
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2 х-3 у=5
3 х+2 у=14

6x-9y=15
6x+4y=28

6x-9y-6x-4y=15-28
-13y= -13
y=1

2x-3×1=5
2x=8
x=4

Answer 2

Solving the System of Equations using the Method of Addition

To solve the system of equations: - 3x + 2y = 3 - 2x + 5y = 13 - 2x - 3y = 5 - 3x + 2y = 14

We can use the method of addition to eliminate one of the variables by adding or subtracting the equations.

Step 1: Eliminating Variable y

To eliminate variable y, we can multiply the third equation by 2 and add it to the first equation: - (3x + 2y) + 2*(2x - 3y) = 3 + 2*5 - 3x + 2y + 4x - 6y = 3 + 10 - 7x - 4y = 13

Now, we have a new equation: 7x - 4y = 13

Step 2: Solving for x

We can now use this new equation and the second equation to solve for x.

Adding the new equation to the second equation: - 7x - 4y + 2x + 5y = 13 + 13 - 9x = 26 - x = 26 / 9 - x = 2.8889

Step 3: Solving for y

Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation: - 3x + 2y = 3 - 3*2.8889 + 2y = 3 - 8.6667 + 2y = 3 - 2y = 3 - 8.6667 - 2y = -5.6667 - y = -2.8333

Solution

The solution to the system of equations is: - x = 2.8889 - y = -2.8333