Question

6( x+y ) = 8+2x-3y 5( y-x ) = 5+3x+2y​

Answer 1

6x+6y=8+2x-3y ; 6x+6y-2x+3y=8; 4x+9y=8 ;

5y-5x=5+3x+2y ; 5y-5x-3x-2y=5;. 3y-8x=5 ;

x=8-9y/4

3y-8*8-9y/4=5

3y-2(8-9y)=5

3y-16+18y=5

21y=5+16

y=1

x=8-9*1/4

x=-1/4

Answer 2

To solve the system of equations:

1. $6(x + y) = 8 + 2x - 3y$
2. $5(y - x) = 5 + 3x + 2y$

We can start by simplifying and isolating variables.

For the first equation:

$6(x + y) = 8 + 2x - 3y$

Distribute the 6:

$6x + 6y = 8 + 2x - 3y$

Rearrange terms:

$4x + 9y = 8$

For the second equation:

$5(y - x) = 5 + 3x + 2y$

Distribute the 5:

$5y - 5x = 5 + 3x + 2y$

Rearrange terms:

$-5x - 3y + 5y - 3x = 5$

$2y - 8x = 5$

Now you have a system of two linear equations:

1. $4x + 9y = 8$
2. $2y - 8x = 5$

From here, you can use methods like substitution, elimination, or matrices to solve for $x$ and $y$. Let's use the substitution method:

From the second equation, isolate $y$:

$2y = 8x + 5$

$y = 4x + \frac{5}{2}$

Now substitute this expression for $y$ into the first equation:

$4x + 9\left(4x + \frac{5}{2}\right) = 8$

$4x + 36x + \frac{45}{2} = 8$

$40x + \frac{45}{2} = 8$

$40x = -\frac{29}{2}$

$x = -\frac{29}{80}$

Now plug this value back into the expression for $y$:

$y = 4\left(-\frac{29}{80}\right) + \frac{5}{2}$

$y = -\frac{29}{40} + \frac{5}{2}$

$y = \frac{91}{40}$

So, the solution to the system of equations is $x = -\frac{29}{80}$ and $y = \frac{91}{40}$.