## Precalculus (6th Edition) Blitzer

The equations modeling the word problem are $3x+2y=8\text{ and }2x-y=3$ and the solution to the system of equations is $\left( x,y \right)=\left( 2,1 \right)$.
Let us assume the first number is x and the second number is y. And addition of three times the first number with twice the second number gives 8. This can be represented by the equation: $3x+2y=8$ And subtraction of the second number from two times the first number gives 3. This can be represented by the equation: $2x-y=3$ And multiply equation $2x-y=3$ by 2 to obtain: $4x-2y=6$ And add equations $3x+2y=8$ and $2x-y=3$: \begin{align} & 3x+2y+4x-2y=8+6 \\ & 7x=14 \\ & x=2 \end{align} Put the value $x=2$ in the equation $3x+2y=8$: \begin{align} & 6+2y=8 \\ & 2y=2 \\ & y=1 \end{align} Thus, the equations modeling the word problem are $3x+2y=8\text{ and }2x-y=3$ and the solution to the system of equations is $\left( x,y \right)=\left( 2,1 \right)$.