Question

3x-y=17 2x+3y=-7 каким способом решить?

Answer 1

{3х - у = 17

{2х + 3у = -7

- - - - - - - - - -

Выразим у через х в первом уравнении и решим систему методом подстановки

{у = 3х - 17

{2х + 3 · (3х - 17) = -7

2х + 9х - 51 = -7

11х = 51 - 7

11х = 44

х = 44 : 11

х = 4

у = 3х - 17 = 3 · 4 - 17 = 12 - 17 = -5

Ответ: (4; -5).      

Answer 2

Solving the System of Equations

To solve the system of equations 3x - y = 17 and 2x + 3y = -7, we can use the method of substitution or the method of elimination. Let's use the method of elimination to solve this system.

Method of Elimination

To eliminate one variable, we can multiply one or both equations by a suitable constant so that the coefficients of one of the variables in both equations become additive inverses (i.e., they add up to zero). In this case, we can multiply the first equation by 3 and the second equation by 2 to make the coefficients of y additive inverses.

Multiplying the first equation by 3, we get:

9x - 3y = 51 (Equation 1)

Multiplying the second equation by 2, we get:

4x + 6y = -14 (Equation 2)

Now, we can add Equation 1 and Equation 2 to eliminate y:

(9x - 3y) + (4x + 6y) = 51 + (-14)

Simplifying the equation, we have:

13x + 3 = 37

Subtracting 3 from both sides, we get:

13x = 34

Dividing both sides by 13, we find:

x = 34/13

Now that we have the value of x, we can substitute it back into one of the original equations to find the value of y. Let's substitute x = 34/13 into the first equation:

3(34/13) - y = 17

Simplifying the equation, we have:

102/13 - y = 17

Subtracting 102/13 from both sides, we get:

-y = 17 - 102/13

Simplifying the right side of the equation, we have:

-y = (221 - 102)/13

-y = 119/13

Dividing both sides by -1, we find:

y = -119/13

Therefore, the solution to the system of equations 3x - y = 17 and 2x + 3y = -7 is x = 34/13 and y = -119/13.