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Solve the system of equations using the elimination method 4x+5y=40 6x+3y=42

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1 vote

Answer:

The solutions to the system of equations are
y=4,\:x=5.

Explanation:

To solve the system
\begin{bmatrix}4x+5y=40\\ 6x+3y=42\end{bmatrix}

First,


\mathrm{Multiply\:}4x+5y=40\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:12x+15y=120\\\\\mathrm{Multiply\:}6x+3y=42\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:12x+6y=84


\begin{bmatrix}12x+15y=120\\ 12x+6y=84\end{bmatrix}

Subtract the first equation from the second equation


12x+6y=84\\\underline{-12x-15y=-120}\\-9y=-36

Solve
-9y=-36 for y:


(-9y)/(-9)=(-36)/(-9)\\y=4

For
12x+15y=12 plug in
y=4 and solve for x


12x+15\cdot \:4=120\\12x=60\\x=5

The solutions to the system of equations are:


y=4,\:x=5

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