Aftrekken geeft \(-y=6\text{,}\) dus \(y=-6\text{.}\)

\(\begin{rcases}3x-6y=3 \\ y=-6\end{rcases}\begin{matrix}3x-6⋅-6=3 \\ 3x=-33 \\ x=-11\end{matrix}\)

De oplossing is \((x, y)=(-11, -6)\text{.}\)

\(\begin{cases}2x-6y=4 \\ x+3y=5\end{cases}\) \(\begin{vmatrix}1 \\ 2\end{vmatrix}\) geeft \(\begin{cases}2x-6y=4 \\ 2x+6y=10\end{cases}\)

Optellen geeft \(4x=14\text{,}\) dus \(x=3\frac{1}{2}\text{.}\)

\(\begin{rcases}2x-6y=4 \\ x=3\frac{1}{2}\end{rcases}\begin{matrix}2⋅3\frac{1}{2}-6y=4 \\ -6y=-3 \\ y=\frac{1}{2}\end{matrix}\)

De oplossing is \((x, y)=(3\frac{1}{2}, \frac{1}{2})\text{.}\)

\(\begin{cases}3a-5b=3 \\ 2a-3b=-5\end{cases}\) \(\begin{vmatrix}3 \\ 5\end{vmatrix}\) geeft \(\begin{cases}9a-15b=9 \\ 10a-15b=-25\end{cases}\)

Aftrekken geeft \(-a=34\text{,}\) dus \(a=-34\text{.}\)

\(\begin{rcases}3a-5b=3 \\ a=-34\end{rcases}\begin{matrix}3⋅-34-5b=3 \\ -5b=105 \\ b=-21\end{matrix}\)

De oplossing is \((a, b)=(-34, -21)\text{.}\)

Gelijk stellen geeft \(3x+14=6x+29\)

\(-3x=15\) dus \(x=-5\)

\(\begin{rcases}y=3x+14 \\ x=-5\end{rcases}\begin{matrix}y=3⋅-5+14 \\ y=-1\end{matrix}\)

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

Substitutie geeft \(8(9q+4)+4q=-44\)

Haakjes wegwerken geeft
\(72q+32+4q=-44\)
\(76q=-76\)
\(q=-1\)

\(\begin{rcases}p=9q+4 \\ q=-1\end{rcases}\begin{matrix}p=9⋅-1+4 \\ p=-5\end{matrix}\)

De oplossing is \((p, q)=(-5, -1)\text{.}\)

Substitutie geeft \(a=8(2a+11)-43\)

Haakjes wegwerken geeft
\(a=16a+88-43\)
\(-15a=45\)
\(a=-3\)

\(\begin{rcases}b=2a+11 \\ a=-3\end{rcases}\begin{matrix}b=2⋅-3+11 \\ b=5\end{matrix}\)

De oplossing is \((a, b)=(-3, 5)\text{.}\)