Getal & Ruimte (13e editie) - vwo wiskunde A
'Stelsels oplossen'.
| vwo wiskunde A | k.1 Stelsels van lineaire vergelijkingen |
opgave 1Los exact op. 3p a \(\begin{cases}2p-4q=4 \\ p+4q=5\end{cases}\) Eliminatie (1) 003f - Stelsels oplossen - basis - 439ms - dynamic variables a Optellen geeft \(3p=9\text{,}\) dus \(p=3\text{.}\) 1p ○ \(\begin{rcases}2p-4q=4 \\ p=3\end{rcases}\begin{matrix}2⋅3-4q=4 \\ -4q=-2 \\ q=\frac{1}{2}\end{matrix}\) 1p ○ De oplossing is \((p, q)=(3, \frac{1}{2})\text{.}\) 1p 4p b \(\begin{cases}2x-y=-4 \\ 3x-3y=6\end{cases}\) Eliminatie (2) 003g - Stelsels oplossen - basis - 21ms - dynamic variables b \(\begin{cases}2x-y=-4 \\ 3x-3y=6\end{cases}\) \(\begin{vmatrix}3 \\ 1\end{vmatrix}\) geeft \(\begin{cases}6x-3y=-12 \\ 3x-3y=6\end{cases}\) 1p ○ Aftrekken geeft \(3x=-18\text{,}\) dus \(x=-6\text{.}\) 1p ○ \(\begin{rcases}2x-y=-4 \\ x=-6\end{rcases}\begin{matrix}2⋅-6-y=-4 \\ -y=8 \\ y=-8\end{matrix}\) 1p ○ De oplossing is \((x, y)=(-6, -8)\text{.}\) 1p 4p c \(\begin{cases}6a+3b=-3 \\ 4a+4b=4\end{cases}\) Eliminatie (3) 003h - Stelsels oplossen - basis - 17ms - dynamic variables c \(\begin{cases}6a+3b=-3 \\ 4a+4b=4\end{cases}\) \(\begin{vmatrix}4 \\ 3\end{vmatrix}\) geeft \(\begin{cases}24a+12b=-12 \\ 12a+12b=12\end{cases}\) 1p ○ Aftrekken geeft \(12a=-24\text{,}\) dus \(a=-2\text{.}\) 1p ○ \(\begin{rcases}6a+3b=-3 \\ a=-2\end{rcases}\begin{matrix}6⋅-2+3b=-3 \\ 3b=9 \\ b=3\end{matrix}\) 1p ○ De oplossing is \((a, b)=(-2, 3)\text{.}\) 1p |