Getal & Ruimte (13e editie) - vwo wiskunde C

'Stelsels oplossen'.

vwo wiskunde A k.1 Stelsels van lineaire vergelijkingen

Stelsels oplossen (3)

opgave 1

Los exact op.

3p

a

\(\begin{cases}2p-2q=-1 \\ 2p-3q=5\end{cases}\)

Eliminatie (1)
003f - Stelsels oplossen - basis - 439ms - dynamic variables

a

Aftrekken geeft \(q=-6\text{.}\)

1p

\(\begin{rcases}2p-2q=-1 \\ q=-6\end{rcases}\begin{matrix}2p-2⋅-6=-1 \\ 2p=-13 \\ p=-6\frac{1}{2}\end{matrix}\)

1p

De oplossing is \((p, q)=(-6\frac{1}{2}, -6)\text{.}\)

1p

4p

b

\(\begin{cases}a+2b=-6 \\ 4a-4b=-6\end{cases}\)

Eliminatie (2)
003g - Stelsels oplossen - basis - 21ms - dynamic variables

b

\(\begin{cases}a+2b=-6 \\ 4a-4b=-6\end{cases}\) \(\begin{vmatrix}2 \\ 1\end{vmatrix}\) geeft \(\begin{cases}2a+4b=-12 \\ 4a-4b=-6\end{cases}\)

1p

Optellen geeft \(6a=-18\text{,}\) dus \(a=-3\text{.}\)

1p

\(\begin{rcases}a+2b=-6 \\ a=-3\end{rcases}\begin{matrix}-3+2b=-6 \\ 2b=-3 \\ b=-1\frac{1}{2}\end{matrix}\)

1p

De oplossing is \((a, b)=(-3, -1\frac{1}{2})\text{.}\)

1p

4p

c

\(\begin{cases}5a-4b=-6 \\ 4a-3b=-4\end{cases}\)

Eliminatie (3)
003h - Stelsels oplossen - basis - 17ms - dynamic variables

c

\(\begin{cases}5a-4b=-6 \\ 4a-3b=-4\end{cases}\) \(\begin{vmatrix}3 \\ 4\end{vmatrix}\) geeft \(\begin{cases}15a-12b=-18 \\ 16a-12b=-16\end{cases}\)

1p

Aftrekken geeft \(-a=-2\text{,}\) dus \(a=2\text{.}\)

1p

\(\begin{rcases}5a-4b=-6 \\ a=2\end{rcases}\begin{matrix}5⋅2-4b=-6 \\ -4b=-16 \\ b=4\end{matrix}\)

1p

De oplossing is \((a, b)=(2, 4)\text{.}\)

1p

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