Question

3 (2x-7y)+5y=62 2 (x+3y)-2y=2 решить систему уравнений

Answer 1

3 (2x-7y)+5y=62 ⇒6x-16y=62

2 (x+3y)-2y=2⇒2x+4y=2 /*4⇒8x+16y=8

прибавим

14x=70

x=5

10+4y=2

4y=-8

y=-2

(5;-2)

Answer 2

To solve the system of equations:

1. 3(2x - 7y) + 5y = 62
2. 2(x + 3y) - 2y = 2

Step 1: Solve the first equation for one variable in terms of the other.

1. 3(2x - 7y) + 5y = 62 Distribute 3 to (2x - 7y): 6x - 21y + 5y = 62 Combine like terms: 6x - 16y = 62 - - - - - - - - - (Equation A)

Step 2: Solve the second equation for one variable in terms of the other.

2. 2(x + 3y) - 2y = 2 Distribute 2 to (x + 3y): 2x + 6y - 2y = 2 Combine like terms: 2x + 4y = 2 - - - - - - - - - (Equation B)

Step 3: Now we have a system of two linear equations with two variables (x and y). We can use the method of substitution or elimination to find the values of x and y.

Method 1: Substitution From Equation A, we can express x in terms of y: 6x = 16y + 62 x = (16y + 62) / 6 x = (8y + 31) / 3

Now substitute this expression for x into Equation B: 2((8y + 31) / 3) + 4y = 2

Method 2: Elimination Multiply Equation B by 3 to eliminate fractions: 3(2x + 4y) = 3(2) 6x + 12y = 6

Now we have the following two equations:

1. 6x - 16y = 62
2. 6x + 12y = 6

Subtract Equation 2 from Equation 1 to eliminate x: (6x - 16y) - (6x + 12y) = 62 - 6 -28y = 56 y = -2

Now that we have the value of y, we can find the value of x using Equation B: 2x + 4y = 2 2x + 4(-2) = 2 2x - 8 = 2 2x = 2 + 8 2x = 10 x = 10 / 2 x = 5

So the solution to the system of equations is: x = 5 y = -2