Question

1217The Elimination MethodSolve the following system of equations with the ELIMINATION METHOD.Write your answer as an Ordered Pair.If infinitely many solutions exist, enter 0 ( infinity)If no solution exists, enter DNESystem of EquationsSolution4x + 8y = 6812x +3y=39

Answer 1

Given: The systems of equation below

`\begin{gathered} 4x+8y=68 \\ 12x+3y=39 \end{gathered}`

To Determine: The solution of the system of equations using elimination method

Eliminate x

To eliminate x, multiply the first equation by 3 and the second equation by 1

`\begin{gathered} 3*(4x+8y=68)=12x+24y=204 \\ 1*(12x+3y=39)=12x+3y=39 \end{gathered}`

Combine two equations by subtracting the second equation from the first

`\begin{gathered} 12x-12x+24y-3y=204-39 \\ 21y=165 \\ (21y)/(21)=(165)/(21) \\ y=(165)/(21)=(55)/(7) \end{gathered}`

Substitute y in the first equation to get x

`\begin{gathered} 4x+8((55)/(7))=68 \\ 4x+(440)/(7)=68 \\ 4x=68-(440)/(7) \\ 4x=(476-440)/(7) \\ 4x=(36)/(7) \\ x=(36)/(7)*(1)/(4) \\ x=(9)/(7) \end{gathered}`

Hence, the solution is

`((9)/(7),(55)/(7))`

(9/7 , 55/7)