Question

2) 1/2(x +11) = 1/3(y +13) + 2, (5x = 3y + 8;

Answer 1

$\left \{ {{\frac{1}{2}(x+11)=\frac{1}{3}(y+13)+2}|*6 \atop {5x=3y+8}} \right.\\\\\left \{ {{3(x+11)=2(y+13)+12} \atop {5x-3y=8}} \right.\\\\\left \{ {{3x+33=2y+26+12} \atop {5x-3y=8}} \right.\\\\\left \{ {{3x-2y=5}|*(-3) \atop {5x-3y=8}|*2} \right.\\\\+\left \{ {{-9x}+6y=-15 \atop {10x-6y=16}} \right.\\--------\\x=1\\\\3y=5x-8=5*1-8=-3\\\\y=-1\\\\Otvet:\boxed{(1;-1)}$

Answer 2

To solve the system of equations:

1. 1/2(x + 11) = 1/3(y + 13) + 2

2. 5x = 3y + 8

We can start by simplifying equation 1:

1/2(x + 11) = 1/3(y + 13) + 2

Multiply both sides of equation 1 by 2 to eliminate the fraction:

x + 11 = 2/3(y + 13) + 4

Multiply both sides by 3 to eliminate the fraction:

3(x + 11) = 2(y + 13) + 12

Expand:

3x + 33 = 2y + 26 + 12

Simplify:

3x + 33 = 2y + 38

Now, we have two simplified equations:

3x + 33 = 2y + 38 ----(3) 5x = 3y + 8 ------------(4)

We can now solve this system of equations using various methods, such as substitution or elimination.

Let's solve it using the substitution method:

From equation (4), we can express y in terms of x:

5x = 3y + 8 3y = 5x - 8 y = (5/3)x - 8/3 ----(5)

Now we substitute equation (5) into equation (3):

3x + 33 = 2((5/3)x - 8/3) + 38

Simplify:

3x + 33 = (10/3)x - (16/3) + 38

Multiply through by 3 to eliminate the fraction:

9x + 99 = 10x - 16 + 114

Simplify further:

9x + 99 = 10x + 98

Subtract 9x from both sides:

99 = x + 98

Subtract 98 from both sides:

1 = x

Now, substitute the value of x back into equation (5) to find y:

y = (5/3)(1) - 8/3 y = 5/3 - 8/3 y = -3/3 y = -1

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