Optellen geeft \(8x=4\text{,}\) dus \(x=\frac{1}{2}\text{.}\)

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

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

\(\begin{cases}a+2b=-2 \\ 2a+5b=3\end{cases}\) \(\begin{vmatrix}2 \\ 1\end{vmatrix}\) geeft \(\begin{cases}2a+4b=-4 \\ 2a+5b=3\end{cases}\)

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

\(\begin{rcases}a+2b=-2 \\ b=7\end{rcases}\begin{matrix}a+2⋅7=-2 \\ a=-16\end{matrix}\)

De oplossing is \((a, b)=(-16, 7)\text{.}\)

\(\begin{cases}2x-5y=-6 \\ 3x-6y=-3\end{cases}\) \(\begin{vmatrix}6 \\ 5\end{vmatrix}\) geeft \(\begin{cases}12x-30y=-36 \\ 15x-30y=-15\end{cases}\)

Aftrekken geeft \(-3x=-21\text{,}\) dus \(x=7\text{.}\)

\(\begin{rcases}2x-5y=-6 \\ x=7\end{rcases}\begin{matrix}2⋅7-5y=-6 \\ -5y=-20 \\ y=4\end{matrix}\)

De oplossing is \((x, y)=(7, 4)\text{.}\)

Gelijk stellen geeft \(3x-1=9x-7\)

\(-6x=-6\) dus \(x=1\)

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

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

Substitutie geeft \(5(9b+19)+2b=1\)

Haakjes wegwerken geeft
\(45b+95+2b=1\)
\(47b=-94\)
\(b=-2\)

\(\begin{rcases}a=9b+19 \\ b=-2\end{rcases}\begin{matrix}a=9⋅-2+19 \\ a=1\end{matrix}\)

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

Substitutie geeft \(p=9(6p-37)+15\)

Haakjes wegwerken geeft
\(p=54p-333+15\)
\(-53p=-318\)
\(p=6\)

\(\begin{rcases}q=6p-37 \\ p=6\end{rcases}\begin{matrix}q=6⋅6-37 \\ q=-1\end{matrix}\)

De oplossing is \((p, q)=(6, -1)\text{.}\)