First, multiply the first equation by 2. That turns the first equation into: 6x - 2y = 18 That way it can easily be added to the second equation: 6x - 2y = 16 x + 2y = 5 --------------- 7x = 21 ========== As you can see, the y disappeared, which was the objective of this operation. Now the equations can be solved easily: 7x = 21 x = 3 Insert x=3 in the original equation: 3*3 - y = 8 9 - y = 8 9 = 8 + y y = 1 So the result is: x = 3 y = 1

[latex]\begin{Bmatrix}3x-y&=&8\\x+2y&=&5\end{matrix}[/latex] Now we can multiply the first row by 2 and add to the second row. [latex]\begin{Bmatrix}3x-y&=&8\\7x&=&21\end{matrix}[/latex] them [latex]\begin{Bmatrix}3x-y&=&8\\x&=&3\end{matrix}[/latex] now we can replace the value in the first row. [latex]\begin{Bmatrix}3*3-y&=&8\\x&=&3\end{matrix}[/latex] [latex]\begin{Bmatrix}-y&=&8-9\\x&=&3\end{matrix}[/latex] [latex]\boxed{\boxed{\begin{Bmatrix}y&=&1\\x&=&3\end{matrix}}}[/latex]