Question

-Solve the system of equations – 5x – 5y = 10 and x + 2y = -3 by combining theequations.1 (- 5x(x–5y = 10)+2y -3)5.2 -5y = 10x +2y = -3tryOo y=With final solution coordinate You must answer all questions above in order to submit.attempt out of 2

Answer 1

We are given the following system of equations:

`\begin{gathered} -5x-5y=10,(1) \\ x+2y=-3,(2) \end{gathered}`

To solve the system we will multiply equation (1) by 1/5, we get:

`((1)/(5))(-5x-5y)=((1)/(5))(10)`

Solving the operations we get:

`-x-y=2`

Now we add this to equation (2):

`-x-y+x+2y=2-3`

Now we associate like terms and solve the operations on the right side:

`(-x+x)+(-y+2y)=-1`

Adding like terms we get:

`\begin{gathered} 0x+(1)y=-1 \\ y=-1 \end{gathered}`

Therefore, the value of "y" is -1. Now we substitute this value in equation (1):

`-x-y=2`

Substituting the value of "y = -1":

`-x-(-1)=2`

Now we solve the operations:

`-x+1=2`

Now we solve for "x" first by subtracting 1 from both sides:

`\begin{gathered} -x+1-1=2-1 \\ -x=1 \end{gathered}`

Now we multiply both sides by -1:

`x=-1`

Therefore, the solution of the system is:

`(x,y)=(-1,-1)`