Getal & Ruimte (13e editie) - vwo wiskunde A
'Stelsels oplossen'.
| vwo wiskunde A | k.1 Stelsels van lineaire vergelijkingen |
opgave 1Los exact op. 3p a \(\begin{cases}3p-6q=3 \\ p-6q=-1\end{cases}\) Eliminatie (1) 003f - Stelsels oplossen - basis - dynamic variables a Aftrekken geeft \(2p=4\text{,}\) dus \(p=2\text{.}\) 1p ○ \(\begin{rcases}3p-6q=3 \\ p=2\end{rcases}\begin{matrix}3⋅2-6q=3 \\ -6q=-3 \\ q=\frac{1}{2}\end{matrix}\) 1p ○ De oplossing is \((p, q)=(2, \frac{1}{2})\text{.}\) 1p 4p b \(\begin{cases}3x+2y=-4 \\ 2x+y=-4\end{cases}\) Eliminatie (2) 003g - Stelsels oplossen - basis - dynamic variables b \(\begin{cases}3x+2y=-4 \\ 2x+y=-4\end{cases}\) \(\begin{vmatrix}1 \\ 2\end{vmatrix}\) geeft \(\begin{cases}3x+2y=-4 \\ 4x+2y=-8\end{cases}\) 1p ○ Aftrekken geeft \(-x=4\text{,}\) dus \(x=-4\text{.}\) 1p ○ \(\begin{rcases}3x+2y=-4 \\ x=-4\end{rcases}\begin{matrix}3⋅-4+2y=-4 \\ 2y=8 \\ y=4\end{matrix}\) 1p ○ De oplossing is \((x, y)=(-4, 4)\text{.}\) 1p 4p c \(\begin{cases}2x+2y=-2 \\ 3x-3y=-6\end{cases}\) Eliminatie (3) 003h - Stelsels oplossen - basis - dynamic variables c \(\begin{cases}2x+2y=-2 \\ 3x-3y=-6\end{cases}\) \(\begin{vmatrix}3 \\ 2\end{vmatrix}\) geeft \(\begin{cases}6x+6y=-6 \\ 6x-6y=-12\end{cases}\) 1p ○ Optellen geeft \(12x=-18\text{,}\) dus \(x=-1\frac{1}{2}\text{.}\) 1p ○ \(\begin{rcases}2x+2y=-2 \\ x=-1\frac{1}{2}\end{rcases}\begin{matrix}2⋅-1\frac{1}{2}+2y=-2 \\ 2y=1 \\ y=\frac{1}{2}\end{matrix}\) 1p ○ De oplossing is \((x, y)=(-1\frac{1}{2}, \frac{1}{2})\text{.}\) 1p |