Question

3(4x−2y+1)−2(5x−y+4)=23 2(x+6y−9)+5(2x−4y+7)=105​

Answer 1

ответ : (4; -5)

решение прикреплено)

Answer 2

To solve this system of equations, let's start by simplifying the given equations step by step.

1. $3(4x - 2y + 1) - 2(5x - y + 4) = 23$

   Expand the equation:

   $12x - 6y + 3 - 10x + 2y - 8 = 23$

   Combine like terms:

   $2x - 4y - 5 = 23$

   $2x - 4y = 28$   (1)

2. $2(x + 6y - 9) + 5(2x - 4y + 7) = 105$

   Expand the equation:

   $2x + 12y - 18 + 10x - 20y + 35 = 105$

   Combine like terms:

   $12x - 8y + 17 = 105$

   $12x - 8y = 88$   (2)

Now you have a system of equations:

$2x - 4y = 28$ $12x - 8y = 88$

You can solve this system using either the substitution method or the elimination method. Let's use the elimination method here.

Multiply equation (1) by 6 and equation (2) by 1 to make the coefficients of $y$ the same:

$12x - 24y = 168$ $12x - 8y = 88$

Subtract the second equation from the first:

$-16y = 80$

Divide by -16:

$y = -5$

Now that you have the value of $y$, substitute it back into equation (1) to solve for $x$:

$2x - 4(-5) = 28$

$2x + 20 = 28$

$2x = 8$

$x = 4$

So the solution to the system of equations is $x = 4$ and $y = -5$.