Aftrekken geeft \(-4a=-2\text{,}\) dus \(a=\frac{1}{2}\text{.}\)

\(\begin{rcases}a-b=-5 \\ a=\frac{1}{2}\end{rcases}\begin{matrix}\frac{1}{2}-b=-5 \\ -b=-5\frac{1}{2} \\ b=5\frac{1}{2}\end{matrix}\)

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

\(\begin{cases}5x-3y=-4 \\ 2x+y=-6\end{cases}\) \(\begin{vmatrix}1 \\ 3\end{vmatrix}\) geeft \(\begin{cases}5x-3y=-4 \\ 6x+3y=-18\end{cases}\)

Optellen geeft \(11x=-22\text{,}\) dus \(x=-2\text{.}\)

\(\begin{rcases}5x-3y=-4 \\ x=-2\end{rcases}\begin{matrix}5⋅-2-3y=-4 \\ -3y=6 \\ y=-2\end{matrix}\)

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

\(\begin{cases}5a+3b=4 \\ 3a+2b=4\end{cases}\) \(\begin{vmatrix}2 \\ 3\end{vmatrix}\) geeft \(\begin{cases}10a+6b=8 \\ 9a+6b=12\end{cases}\)

Aftrekken geeft \(a=-4\text{.}\)

\(\begin{rcases}5a+3b=4 \\ a=-4\end{rcases}\begin{matrix}5⋅-4+3b=4 \\ 3b=24 \\ b=8\end{matrix}\)

De oplossing is \((a, b)=(-4, 8)\text{.}\)

Gelijk stellen geeft \(8x-30=2x-6\)

\(6x=24\) dus \(x=4\)

\(\begin{rcases}y=8x-30 \\ x=4\end{rcases}\begin{matrix}y=8⋅4-30 \\ y=2\end{matrix}\)

De oplossing is \((x, y)=(4, 2)\text{.}\)

Substitutie geeft \(4(9q-48)+5q=13\)

Haakjes wegwerken geeft
\(36q-192+5q=13\)
\(41q=205\)
\(q=5\)

\(\begin{rcases}p=9q-48 \\ q=5\end{rcases}\begin{matrix}p=9⋅5-48 \\ p=-3\end{matrix}\)

De oplossing is \((p, q)=(-3, 5)\text{.}\)

Substitutie geeft \(y=6(3y+5)+21\)

Haakjes wegwerken geeft
\(y=18y+30+21\)
\(-17y=51\)
\(y=-3\)

\(\begin{rcases}x=3y+5 \\ y=-3\end{rcases}\begin{matrix}x=3⋅-3+5 \\ x=-4\end{matrix}\)

De oplossing is \((x, y)=(-4, -3)\text{.}\)