Stelsels oplossen

Aftrekken geeft \(-a=7\text{,}\) dus \(a=-7\text{.}\)

\(\begin{rcases}2a-b=5 \\ a=-7\end{rcases}\begin{matrix}2⋅-7-b=5 \\ -b=19 \\ b=-19\end{matrix}\)

De oplossing is \((a, b)=(-7, -19)\text{.}\)

\(\begin{cases}5a+5b=5 \\ 3a+b=-5\end{cases}\) \(\begin{vmatrix}1 \\ 5\end{vmatrix}\) geeft \(\begin{cases}5a+5b=5 \\ 15a+5b=-25\end{cases}\)

Aftrekken geeft \(-10a=30\text{,}\) dus \(a=-3\text{.}\)

\(\begin{rcases}5a+5b=5 \\ a=-3\end{rcases}\begin{matrix}5⋅-3+5b=5 \\ 5b=20 \\ b=4\end{matrix}\)

De oplossing is \((a, b)=(-3, 4)\text{.}\)

\(\begin{cases}2x+2y=-6 \\ 5x-3y=5\end{cases}\) \(\begin{vmatrix}3 \\ 2\end{vmatrix}\) geeft \(\begin{cases}6x+6y=-18 \\ 10x-6y=10\end{cases}\)

Optellen geeft \(16x=-8\text{,}\) dus \(x=-\frac{1}{2}\text{.}\)

\(\begin{rcases}2x+2y=-6 \\ x=-\frac{1}{2}\end{rcases}\begin{matrix}2⋅-\frac{1}{2}+2y=-6 \\ 2y=-5 \\ y=-2\frac{1}{2}\end{matrix}\)

De oplossing is \((x, y)=(-\frac{1}{2}, -2\frac{1}{2})\text{.}\)

Gelijk stellen geeft \(3y-6=6y-9\)

\(-3y=-3\) dus \(y=1\)

\(\begin{rcases}x=3y-6 \\ y=1\end{rcases}\begin{matrix}x=3⋅1-6 \\ x=-3\end{matrix}\)

De oplossing is \((x, y)=(-3, 1)\text{.}\)

Substitutie geeft \(5p+4(2p-8)=46\)

Haakjes wegwerken geeft
\(5p+8p-32=46\)
\(13p=78\)
\(p=6\)

\(\begin{rcases}q=2p-8 \\ p=6\end{rcases}\begin{matrix}q=2⋅6-8 \\ q=4\end{matrix}\)

De oplossing is \((p, q)=(6, 4)\text{.}\)

Substitutie geeft \(x=8(5x-24)-3\)

Haakjes wegwerken geeft
\(x=40x-192-3\)
\(-39x=-195\)
\(x=5\)

\(\begin{rcases}y=5x-24 \\ x=5\end{rcases}\begin{matrix}y=5⋅5-24 \\ y=1\end{matrix}\)

De oplossing is \((x, y)=(5, 1)\text{.}\)