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Find the solution to the following system of equations. x-2/3y=8 -1/5x+1/3y = 3

User Pschwamb
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Note: Your question sounds a little unclear, but I am assuming that your system of equations is:


x-(2)/(3)y=8


-(1)/(5)x+(1)/(3)y\:=\:3

It would anyways clear your concept because the procedure to find the solutions remains the same for any set of a system of equations.

Answer:

The solution of the system of equations be:


x=(70)/(3),\:y=23

Explanation:

Given the system of equations


\begin{bmatrix}x-(2)/(3)y=8\\ -(1)/(5)x+(1)/(3)y=3\end{bmatrix}


\mathrm{Multiply\:}-(1)/(5)x+(1)/(3)y=3\mathrm{\:by\:}5\:\mathrm{:}\:\quad \:-x+(5)/(3)y=15


\begin{bmatrix}x-(2)/(3)y=8\\ -x+(5)/(3)y=15\end{bmatrix}

so adding the equation


-x+(5)/(3)y=15


+


\underline{x-(2)/(3)y=8}


y=23

so the system equations become


\begin{bmatrix}x-(2)/(3)y=8\\ y=23\end{bmatrix}


\mathrm{For\:}x-(2)/(3)y=8\mathrm{\:plug\:in\:}y=23


x-(2)/(3)\cdot \:23=8


x-(46)/(3)=8

Add 46/3 to both sides


x-(46)/(3)+(46)/(3)=8+(46)/(3)


x=(70)/(3)

Therefore, the solution of the system of equations be:


x=(70)/(3),\:y=23

User Quastiat
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