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What choice is a solution to the system of equations? y=2x-3 y-9=-x

User Homebase
by
3.5k points

2 Answers

14 votes

Answer:


(4,5)\ or\ x=4,y=5

Explanation:


We\ are\ given:\\y=2x-3\\y-9=-x\\Now,\ lets\ separate\ all\ the\ constant\ terms\ to\ the\ RHS\ and\ the\ variable\\ terms\ to\ the\ LHS.\\Hence,\\y-2x=-3\\y+x=9\\By\ subtracting\ the\ two\ equations:\\(y-2x)-(y+x)=(-3)-(9)\\Hence\ lets\ simplify\ this\ main\ equation: \\y-2x-(y+x)=-3-9\\y-2x-y-x=-12\\-3x=-12\\x=(-12)/(-3)=4\\\\Now,\ lets\ consider\ the\ second\ equation\ in\ the\ solution:\\y-9=-x\\Substituting\ x=4,\\y-9=-(4)\\y-9=-4\\y=-4+9\\y=5\\


Now,\\We\ get\ the\ solution\ to\ this\ system\ of\ equations:\\x=4,y=5\\By\ putting\ this\ as\ a\ co-ordinate\ pair (x,y):\\(4,5)

User Omar Aflak
by
3.8k points
12 votes

Answer:

The solution of the system of equations will be:


y=5,\:x=4

Explanation:

Given the system of equation


\begin{bmatrix}y=2x-3\\ y-9=-x\end{bmatrix}

Arrange equation variables for elimination


\begin{bmatrix}y-2x=-3\\ y+x=9\end{bmatrix}

so


y+x=9


-


\underline{y-2x=-3}


3x=12

so the system of equations becomes


\begin{bmatrix}y-2x=-3\\ 3x=12\end{bmatrix}

solve 3x=12 for x


3x=12

Divide both sides by 3


(3x)/(3)=(12)/(3)


x=4


\mathrm{For\:}y-2x=-3\mathrm{\:plug\:in\:}x=4


y-2\cdot \:4=-3


y-8=-3

Add 8 to both sides


y-8+8=-3+8


y=5

Thus, the solution of the system of equations will be:


y=5,\:x=4

User Donshikin
by
3.4k points