Aftrekken geeft \(3a=-6\text{,}\) dus \(a=-2\text{.}\)

\(\begin{rcases}4a-b=-3 \\ a=-2\end{rcases}\begin{matrix}4⋅-2-b=-3 \\ -b=5 \\ b=-5\end{matrix}\)

De oplossing is \((a, b)=(-2, -5)\text{.}\)

\(\begin{cases}6p-4q=1 \\ 3p+q=2\end{cases}\) \(\begin{vmatrix}1 \\ 4\end{vmatrix}\) geeft \(\begin{cases}6p-4q=1 \\ 12p+4q=8\end{cases}\)

Optellen geeft \(18p=9\text{,}\) dus \(p=\frac{1}{2}\text{.}\)

\(\begin{rcases}6p-4q=1 \\ p=\frac{1}{2}\end{rcases}\begin{matrix}6⋅\frac{1}{2}-4q=1 \\ -4q=-2 \\ q=\frac{1}{2}\end{matrix}\)

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

\(\begin{cases}6a+6b=3 \\ 5a+4b=-3\end{cases}\) \(\begin{vmatrix}2 \\ 3\end{vmatrix}\) geeft \(\begin{cases}12a+12b=6 \\ 15a+12b=-9\end{cases}\)

Aftrekken geeft \(-3a=15\text{,}\) dus \(a=-5\text{.}\)

\(\begin{rcases}6a+6b=3 \\ a=-5\end{rcases}\begin{matrix}6⋅-5+6b=3 \\ 6b=33 \\ b=5\frac{1}{2}\end{matrix}\)

De oplossing is \((a, b)=(-5, 5\frac{1}{2})\text{.}\)

Gelijk stellen geeft \(2x+9=5x+18\)

\(-3x=9\) dus \(x=-3\)

\(\begin{rcases}y=2x+9 \\ x=-3\end{rcases}\begin{matrix}y=2⋅-3+9 \\ y=3\end{matrix}\)

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

Substitutie geeft \(6(7y+43)+9y=-48\)

Haakjes wegwerken geeft
\(42y+258+9y=-48\)
\(51y=-306\)
\(y=-6\)

\(\begin{rcases}x=7y+43 \\ y=-6\end{rcases}\begin{matrix}x=7⋅-6+43 \\ x=1\end{matrix}\)

De oplossing is \((x, y)=(1, -6)\text{.}\)

Substitutie geeft \(x=6(2x-5)+19\)

Haakjes wegwerken geeft
\(x=12x-30+19\)
\(-11x=-11\)
\(x=1\)

\(\begin{rcases}y=2x-5 \\ x=1\end{rcases}\begin{matrix}y=2⋅1-5 \\ y=-3\end{matrix}\)

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