Aftrekken geeft \(-3x=-9\text{,}\) dus \(x=3\text{.}\)

\(\begin{rcases}3x-6y=-3 \\ x=3\end{rcases}\begin{matrix}3⋅3-6y=-3 \\ -6y=-12 \\ y=2\end{matrix}\)

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

\(\begin{cases}4a+2b=-3 \\ 3a-b=-1\end{cases}\) \(\begin{vmatrix}1 \\ 2\end{vmatrix}\) geeft \(\begin{cases}4a+2b=-3 \\ 6a-2b=-2\end{cases}\)

Optellen geeft \(10a=-5\text{,}\) dus \(a=-\frac{1}{2}\text{.}\)

\(\begin{rcases}4a+2b=-3 \\ a=-\frac{1}{2}\end{rcases}\begin{matrix}4⋅-\frac{1}{2}+2b=-3 \\ 2b=-1 \\ b=-\frac{1}{2}\end{matrix}\)

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

\(\begin{cases}3p+5q=-5 \\ 4p+6q=-3\end{cases}\) \(\begin{vmatrix}6 \\ 5\end{vmatrix}\) geeft \(\begin{cases}18p+30q=-30 \\ 20p+30q=-15\end{cases}\)

Aftrekken geeft \(-2p=-15\text{,}\) dus \(p=7\frac{1}{2}\text{.}\)

\(\begin{rcases}3p+5q=-5 \\ p=7\frac{1}{2}\end{rcases}\begin{matrix}3⋅7\frac{1}{2}+5q=-5 \\ 5q=-27\frac{1}{2} \\ q=-5\frac{1}{2}\end{matrix}\)

De oplossing is \((p, q)=(7\frac{1}{2}, -5\frac{1}{2})\text{.}\)

Gelijk stellen geeft \(4x+11=2x+7\)

\(2x=-4\) dus \(x=-2\)

\(\begin{rcases}y=4x+11 \\ x=-2\end{rcases}\begin{matrix}y=4⋅-2+11 \\ y=3\end{matrix}\)

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

Substitutie geeft \(8x+2(3x-9)=52\)

Haakjes wegwerken geeft
\(8x+6x-18=52\)
\(14x=70\)
\(x=5\)

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

De oplossing is \((x, y)=(5, 6)\text{.}\)

Substitutie geeft \(a=9(3a+8)+6\)

Haakjes wegwerken geeft
\(a=27a+72+6\)
\(-26a=78\)
\(a=-3\)

\(\begin{rcases}b=3a+8 \\ a=-3\end{rcases}\begin{matrix}b=3⋅-3+8 \\ b=-1\end{matrix}\)

De oplossing is \((a, b)=(-3, -1)\text{.}\)