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

\(\begin{cases}4 p + q = -6 \\ 3 p + q = -3\end{cases}\)

Eliminatie (1)
003f - Stelsels oplossen - basis - 306ms - dynamic variables

a

Aftrekken geeft \(p = -3 \text{.}\)

1p

○

\(\begin{rcases}4 p + q = -6 \\ p = -3\end{rcases} \begin{matrix}4 ⋅ -3 + q = -6 \\ q = 6\end{matrix}\)

1p

○

De oplossing is \((p , q) = (-3 , 6) \text{.}\)

1p

4p

b

\(\begin{cases}5 x + 3 y = -6 \\ x - y = -6\end{cases}\)

Eliminatie (2)
003g - Stelsels oplossen - basis - 12ms - dynamic variables

b

\(\begin{cases}5 x + 3 y = -6 \\ x - y = -6\end{cases}\) \(\begin{vmatrix}1 \\ 3\end{vmatrix}\) geeft \(\begin{cases}5 x + 3 y = -6 \\ 3 x - 3 y = -18\end{cases}\)

1p

○

Optellen geeft \(8 x = -24 \text{,}\) dus \(x = -3 \text{.}\)

1p

○

\(\begin{rcases}5 x + 3 y = -6 \\ x = -3\end{rcases} \begin{matrix}5 ⋅ -3 + 3 y = -6 \\ 3 y = 9 \\ y = 3\end{matrix}\)

1p

○

De oplossing is \((x , y) = (-3 , 3) \text{.}\)

1p

4p

c

\(\begin{cases}4 x - 2 y = 4 \\ 3 x - 3 y = -6\end{cases}\)

Eliminatie (3)
003h - Stelsels oplossen - basis - 11ms - dynamic variables

c

\(\begin{cases}4 x - 2 y = 4 \\ 3 x - 3 y = -6\end{cases}\) \(\begin{vmatrix}3 \\ 2\end{vmatrix}\) geeft \(\begin{cases}12 x - 6 y = 12 \\ 6 x - 6 y = -12\end{cases}\)

1p

○

Aftrekken geeft \(6 x = 24 \text{,}\) dus \(x = 4 \text{.}\)

1p

○

\(\begin{rcases}4 x - 2 y = 4 \\ x = 4\end{rcases} \begin{matrix}4 ⋅ 4 - 2 y = 4 \\ -2 y = -12 \\ y = 6\end{matrix}\)

1p

○

De oplossing is \((x , y) = (4 , 6) \text{.}\)

1p

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