Question

Determine whether the given ordered pair is a solution to the system of equations. 6x−2y =34−3x+3y =15 and (11,16) ____Yes, it is a solution.____ No, it is not a solution.

Answer 1

Given:

`\begin{gathered} 6x-2y=34\ldots\ldots\ldots\text{.}\mathrm{}(1) \\ -3x+3y=15\ldots\ldots\ldots\text{.}(2) \end{gathered}`

Sol:.

Mutiply by 2 in equation (2) then.

`\begin{gathered} -3x+3y=15 \\ 2(-3x+3y)=2*15 \\ -6x+6y=30 \end{gathered}`

Add both equation then:

`\begin{gathered} 6x-2y=34 \\ -6x+6y=30 \\ \text{Add both equation:} \\ 6x-2y+(-6x)+6y=34+30 \\ 6x-6x+6y-2y=34+30 \\ 6y-2y=64 \\ 4y=64 \\ y=(64)/(4) \\ y=16 \end{gathered}`

Put the value of y for find the value od "x"

`\begin{gathered} 6x-2y=34 \\ y=16 \\ 6x-2(16)=34 \\ 6x-32=34 \\ 6x=34+32 \\ 6x=66 \\ x=(66)/(6) \\ x=11 \end{gathered}`

So the value of "x" is 11 and value of "y" is 16 then:

`\text{solution =(11,16)}`