Question

3x+7y=-1 2x-3y=7 метод алгебраического сложения, помогите

Answer 1

3x+7y= -1 /*3⇒9x+21y=-3
2x-3y= 7 /7⇒14x-21y=49
прибавим
23x=46
x=2
6+7y=-1
7y=-7
y=-1
(2;-1)

Answer 2

Solving the System of Equations

To solve the system of equations 3x + 7y = -1 and 2x - 3y = 7 using the method of algebraic addition, we can eliminate one variable by adding or subtracting the equations. Let's go step by step:

Step 1: Multiply the first equation by 2 and the second equation by 3 to make the coefficients of x in both equations the same: - Equation 1: 6x + 14y = -2 - Equation 2: 6x - 9y = 21

Step 2: Subtract Equation 2 from Equation 1 to eliminate x: - (6x + 14y) - (6x - 9y) = (-2) - 21 - Simplifying, we get: 23y = 19

Step 3: Solve for y by dividing both sides of the equation by 23: - y = 19/23

Step 4: Substitute the value of y back into one of the original equations to solve for x. Let's use the first equation: - 3x + 7(19/23) = -1 - Simplifying, we get: 3x + (133/23) = -1 - Subtracting (133/23) from both sides, we get: 3x = -1 - (133/23) - Simplifying further, we get: 3x = (-23 - 133)/23 - Simplifying, we get: 3x = -156/23 - Dividing both sides by 3, we get: x = (-156/23) / 3 - Simplifying, we get: x = -156/69

Therefore, the solution to the system of equations 3x + 7y = -1 and 2x - 3y = 7 is x = -156/69 and y = 19/23.

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