Question

Решить систему с помощью способа сложения.Распишите решение пожалуйста полностью.1){3x+2y=5 -5x+2y=452){9x-4y=-13 9x-2y=-203){12x-7y=2 4x-5y=6

Answer 1

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Answer 2

1){3x+2y=5 умножаем на (-1)
-5x+2y=45

{-3x-2y=-5
+
-5x+2y=45

-3x+(-5x)-2y+2y=-5+45
-8x=40
-x=40/8
-x=5
x=-5

Answer 3

Solving the System of Equations using the Method of Addition

To solve the given system of equations using the method of addition, we will add the equations together in such a way that one of the variables cancels out. Let's go through the solution step by step:

Step 1: Write down the given system of equations: 1) 3x + 2y = 5 -5x + 2y = 45

2) 9x - 4y = -13 9x - 2y = -20

3) 12x - 7y = 2 4x - 5y = 6

Step 2: Choose two equations to add together. In this case, let's choose equations 1) and 2) to eliminate the variable 'y'.

Step 3: Multiply one or both equations by a constant so that the coefficients of 'y' in both equations are the same. In this case, we can multiply equation 1) by 2 and equation 2) by -1 to achieve this:

2(3x + 2y) = 2(5) -1(9x - 4y) = -1(-13)

Simplifying these equations, we get: 6x + 4y = 10 -9x + 4y = 13

Step 4: Add the two equations together to eliminate the variable 'y': (6x + 4y) + (-9x + 4y) = 10 + 13

Simplifying this equation, we get: -3x = 23

Step 5: Solve for 'x': Divide both sides of the equation by -3: -3x / -3 = 23 / -3 x = -23/3

Step 6: Substitute the value of 'x' back into one of the original equations to solve for 'y'. Let's use equation 1): 3(-23/3) + 2y = 5

Simplifying this equation, we get: -23 + 2y = 5

Step 7: Solve for 'y': Add 23 to both sides of the equation: -23 + 23 + 2y = 5 + 23 2y = 28

Divide both sides of the equation by 2: 2y / 2 = 28 / 2 y = 14

Step 8: Check the solution by substituting the values of 'x' and 'y' back into the other equations. Let's check using equation 2): 9x - 4y = -13 9(-23/3) - 4(14) = -13

Simplifying this equation, we get: -207/3 - 56 = -13 -69 - 56 = -13 -125 = -13

The equation is true, which means the solution (x = -23/3, y = 14) satisfies all the original equations.

Therefore, the solution to the given system of equations is: x = -23/3 y = 14