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

'Stelsels oplossen'.

vwo wiskunde A k.1 Stelsels van lineaire vergelijkingen

Stelsels oplossen (3)

opgave 1

Los 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

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