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

\(\begin{rcases}2x-2y=-6 \\ x=-1\frac{1}{2}\end{rcases}\begin{matrix}2⋅-1\frac{1}{2}-2y=-6 \\ -2y=-3 \\ y=1\frac{1}{2}\end{matrix}\)

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

\(\begin{cases}6a-3b=3 \\ 4a-b=-5\end{cases}\) \(\begin{vmatrix}1 \\ 3\end{vmatrix}\) geeft \(\begin{cases}6a-3b=3 \\ 12a-3b=-15\end{cases}\)

Aftrekken geeft \(-6a=18\text{,}\) dus \(a=-3\text{.}\)

\(\begin{rcases}6a-3b=3 \\ a=-3\end{rcases}\begin{matrix}6⋅-3-3b=3 \\ -3b=21 \\ b=-7\end{matrix}\)

De oplossing is \((a, b)=(-3, -7)\text{.}\)

\(\begin{cases}4x+3y=2 \\ 6x+5y=5\end{cases}\) \(\begin{vmatrix}5 \\ 3\end{vmatrix}\) geeft \(\begin{cases}20x+15y=10 \\ 18x+15y=15\end{cases}\)

Aftrekken geeft \(2x=-5\text{,}\) dus \(x=-2\frac{1}{2}\text{.}\)

\(\begin{rcases}4x+3y=2 \\ x=-2\frac{1}{2}\end{rcases}\begin{matrix}4⋅-2\frac{1}{2}+3y=2 \\ 3y=12 \\ y=4\end{matrix}\)

De oplossing is \((x, y)=(-2\frac{1}{2}, 4)\text{.}\)

Gelijk stellen geeft \(8x-11=2x-5\)

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

\(\begin{rcases}y=8x-11 \\ x=1\end{rcases}\begin{matrix}y=8⋅1-11 \\ y=-3\end{matrix}\)

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

Substitutie geeft \(5(6b-41)+9b=29\)

Haakjes wegwerken geeft
\(30b-205+9b=29\)
\(39b=234\)
\(b=6\)

\(\begin{rcases}a=6b-41 \\ b=6\end{rcases}\begin{matrix}a=6⋅6-41 \\ a=-5\end{matrix}\)

De oplossing is \((a, b)=(-5, 6)\text{.}\)

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

Haakjes wegwerken geeft
\(p=54p+90-37\)
\(-53p=53\)
\(p=-1\)

\(\begin{rcases}q=9p+15 \\ p=-1\end{rcases}\begin{matrix}q=9⋅-1+15 \\ q=6\end{matrix}\)

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