Question

what is the solution of each system ? use elimination 5x-6y=-32-3x-3y=9

Answer 1

Answer:

x = -50/11

y = 17/11

Explanation:

We have the following system of equations:

5x - 6y = -32

-3x - 3y = 9

To solve by elimination, we will multiply both sides of the second equation by -2, so:

$\begin{gathered} -2(-3x-3y)=-2(9) \\ -2(-3x)-2(-3y)=-18 \\ 6x+6y=-18 \end{gathered}$

Now, we can add this equation with the first equation, so:

5x - 6x = -32

6x + 6x = -18

11x + 0 = -50

So, solving for x, we get:

11x = - 50

11x/11 = -50/11

x = -50/11

Then, we can replace the value of x by -50/11 on the first equation:

$\begin{gathered} 5x-6y=-32 \\ 5(-\frac{50}{11})-6y=-32 \end{gathered}$

So, solving for y, we get:

$\begin{gathered} -\frac{250}{11}-6y=-32 \\ -\frac{250}{11}-6y+\frac{250}{11}=-32+\frac{250}{11} \\ -6y=-\frac{102}{11} \\ \frac{-6y}{-6}=\frac{-102}{11}\cdot\frac{1}{-6} \\ y=\frac{17}{11} \end{gathered}$

Therefore, the solution of the system is:

x = -50/11

y = 17/11