Question

3(x-2)-2(y+1)=-1 5(x+3)-8(y-2)=45 решить систему​

Answer 1

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Answer 2

To solve the system of equations:

1. 3(x - 2) - 2(y + 1) = -1
2. 5(x + 3) - 8(y - 2) = 45

We'll use the method of substitution. Let's solve equation 1 for x:

3(x - 2) - 2(y + 1) = -1 3x - 6 - 2y - 2 = -1 3x - 2y - 8 = -1 3x - 2y = 7 ----(3)

Now, substitute equation 3 into equation 2:

5(x + 3) - 8(y - 2) = 45 5x + 15 - 8(y - 2) = 45 5x - 8y + 16 = 45 5x - 8y = 29 ----(4)

Now we have a system of two equations:

3x - 2y = 7 ----(3) 5x - 8y = 29 ----(4)

To solve this system, we can use the method of elimination. Multiply equation 3 by 5 and equation 4 by 3 to eliminate x:

15x - 10y = 35 ----(5) 15x - 24y = 87 ----(6)

Subtract equation 6 from equation 5:

(15x - 10y) - (15x - 24y) = 35 - 87 15x - 10y - 15x + 24y = -52 14y = -52 y = -52/14 y = -26/7

Now substitute the value of y back into equation 3 to solve for x:

3x - 2(-26/7) = 7 3x + 52/7 = 7 3x = 7 - 52/7 3x = 49/7 - 52/7 3x = -3/7 x = -1/7

Therefore, the solution to the system of equations is x = -1/7 and y = -26/7.