Optellen geeft \(6x=-9\text{,}\) dus \(x=-1\frac{1}{2}\text{.}\)

\(\begin{rcases}2x+4y=-5 \\ x=-1\frac{1}{2}\end{rcases}\begin{matrix}2⋅-1\frac{1}{2}+4y=-5 \\ 4y=-2 \\ y=-\frac{1}{2}\end{matrix}\)

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

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

Aftrekken geeft \(p=-7\text{.}\)

\(\begin{rcases}2p+2q=-3 \\ p=-7\end{rcases}\begin{matrix}2⋅-7+2q=-3 \\ 2q=11 \\ q=5\frac{1}{2}\end{matrix}\)

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

\(\begin{cases}3a-4b=-6 \\ 2a-3b=5\end{cases}\) \(\begin{vmatrix}3 \\ 4\end{vmatrix}\) geeft \(\begin{cases}9a-12b=-18 \\ 8a-12b=20\end{cases}\)

Aftrekken geeft \(a=-38\text{.}\)

\(\begin{rcases}3a-4b=-6 \\ a=-38\end{rcases}\begin{matrix}3⋅-38-4b=-6 \\ -4b=108 \\ b=-27\end{matrix}\)

De oplossing is \((a, b)=(-38, -27)\text{.}\)

Gelijk stellen geeft \(6x-13=9x-22\)

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

\(\begin{rcases}y=6x-13 \\ x=3\end{rcases}\begin{matrix}y=6⋅3-13 \\ y=5\end{matrix}\)

De oplossing is \((x, y)=(3, 5)\text{.}\)

Substitutie geeft \(5a+3(7a-3)=17\)

Haakjes wegwerken geeft
\(5a+21a-9=17\)
\(26a=26\)
\(a=1\)

\(\begin{rcases}b=7a-3 \\ a=1\end{rcases}\begin{matrix}b=7⋅1-3 \\ b=4\end{matrix}\)

De oplossing is \((a, b)=(1, 4)\text{.}\)

Substitutie geeft \(y=2(4y+18)-15\)

Haakjes wegwerken geeft
\(y=8y+36-15\)
\(-7y=21\)
\(y=-3\)

\(\begin{rcases}x=4y+18 \\ y=-3\end{rcases}\begin{matrix}x=4⋅-3+18 \\ x=6\end{matrix}\)

De oplossing is \((x, y)=(6, -3)\text{.}\)