Question

3(x+y)-4(x-y)=54(x+y)-3(x-y)=9​

Answer 1

Ответ:

3(x+y)-4(x-y)=5

4(x+y)-3(x-y)=9

3x+3y-4x+4y=5

4x+4y-3x+3y=9

-x+7y=5

x+7y=9

-x+7y=5

x=9-7y

-(9-7y)+7y=5

-9+7y+7y=5

14y=5+9

14y=14

y=14÷14

y=1

x=9-7×1

x=2

ответ:

(x;y)=(2;1)

Answer 2

To solve the system of equations, let's first simplify each equation:

1. $3(x + y) - 4(x - y) = 54$

Distribute the constants:

$3x + 3y - 4x + 4y = 54$

Combine like terms:

$-x + 7y = 54$

2. $54(x + y) - 3(x - y) = 9$

Distribute the constants:

$54x + 54y - 3x + 3y = 9$

Combine like terms:

$51x + 57y = 9$

Now you have a system of two equations:

1. $-x + 7y = 54$
2. $51x + 57y = 9$

To solve this system, you can use the substitution method, elimination method, or matrices. Let's use the elimination method to eliminate $y$:

Multiply the first equation by 57 and the second equation by 7 to make the coefficients of $y$ the same:

1. $-57x + 399y = 3086$
2. $357x + 399y = 63$

Now, add the two equations to eliminate $y$:

$-57x + 399y + 357x + 399y = 3086 + 63$

Combine like terms:

$300x + 798y = 3149$

Now, you have two equations:

1. $-x + 7y = 54$
2. $300x + 798y = 3149$

You can now solve this system of equations to find the values of $x$ and $y$.