Question

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

Answer 1

x = -50/11

y = 17/11

Step-by-step 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(-(50)/(11))-6y=-32 \end{gathered}`

So, solving for y, we get:

`\begin{gathered} -(250)/(11)-6y=-32 \\ -(250)/(11)-6y+(250)/(11)=-32+(250)/(11) \\ -6y=-(102)/(11) \\ (-6y)/(-6)=(-102)/(11)\cdot(1)/(-6) \\ y=(17)/(11) \end{gathered}`

Therefore, the solution of the system is:

x = -50/11

y = 17/11