Question

For each ordered pair, determine whether it is a solution to the system of equations -5x+4y=2. 3x-5y=4 solution? (x, y) (6,8) it is a solution yes or no. (-4,-4) it is a solutions yes or no. (-7,0) it is a solution yes or no. (3,1) it is a solution yes or no

Answer 1

`\mleft\{\begin{aligned}-5x+4y=2 \\ 3x-5y=4\end{aligned}\mright.`

Check the solutions

(6,8)

(-4,-4)

(-7,0)

(3,1)

To check if the pair is a solution to teh system of equations you must replace x and y on both of the equations and see if the equation is fulfilled

(6,8) Is not a solution to the system of a solutions

`\begin{gathered} \begin{aligned}-5(6)+4(8)=2 \\ 3(6)-5(8)=4\end{aligned} \\ \\ -30+32=2\longrightarrow2=2 \\ 18-40=4\longrightarrow-22\\e4 \end{gathered}`

(-4,-4) is not a solution to the system of equations

`\begin{gathered} \begin{aligned}-5(-4)+4(-4)=2 \\ 3(-4)-5(-4)=4\end{aligned} \\ \\ 20-16=2\longrightarrow4\\e2 \\ -12+16=4\longrightarrow4=4 \end{gathered}`

(-7,0) is not a solution to the system of equations

`\begin{gathered} \begin{aligned}-5(-7)+4(0)=2 \\ 3(-7)-5(0)=4\end{aligned} \\ \\ 35+0=2\longrightarrow35\\e2 \\ -21-0=4-21\\e4 \end{gathered}`

(3,1) is not a solution to the system of equations

`\begin{gathered} \begin{aligned}-5(3)+4(1)=2 \\ 3(3)-5(1)=4\end{aligned} \\ \\ -15+4=2\longrightarrow-11\\e2 \\ 9-5=4\longrightarrow4=4 \end{gathered}`