Aftrekken geeft \(-2b=4\text{,}\) dus \(b=-2\text{.}\)

\(\begin{rcases}a+b=6 \\ b=-2\end{rcases}\begin{matrix}a-2=6 \\ a=8\end{matrix}\)

De oplossing is \((a, b)=(8, -2)\text{.}\)

\(\begin{cases}5a-4b=1 \\ 3a-2b=-6\end{cases}\) \(\begin{vmatrix}1 \\ 2\end{vmatrix}\) geeft \(\begin{cases}5a-4b=1 \\ 6a-4b=-12\end{cases}\)

Aftrekken geeft \(-a=13\text{,}\) dus \(a=-13\text{.}\)

\(\begin{rcases}5a-4b=1 \\ a=-13\end{rcases}\begin{matrix}5⋅-13-4b=1 \\ -4b=66 \\ b=-16\frac{1}{2}\end{matrix}\)

De oplossing is \((a, b)=(-13, -16\frac{1}{2})\text{.}\)

\(\begin{cases}4x+2y=1 \\ 3x-3y=3\end{cases}\) \(\begin{vmatrix}3 \\ 2\end{vmatrix}\) geeft \(\begin{cases}12x+6y=3 \\ 6x-6y=6\end{cases}\)

Optellen geeft \(18x=9\text{,}\) dus \(x=\frac{1}{2}\text{.}\)

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

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

Gelijk stellen geeft \(5x-24=9x-40\)

\(-4x=-16\) dus \(x=4\)

\(\begin{rcases}y=5x-24 \\ x=4\end{rcases}\begin{matrix}y=5⋅4-24 \\ y=-4\end{matrix}\)

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

Substitutie geeft \(4(7q-31)+5q=41\)

Haakjes wegwerken geeft
\(28q-124+5q=41\)
\(33q=165\)
\(q=5\)

\(\begin{rcases}p=7q-31 \\ q=5\end{rcases}\begin{matrix}p=7⋅5-31 \\ p=4\end{matrix}\)

De oplossing is \((p, q)=(4, 5)\text{.}\)

Substitutie geeft \(x=4(8x+9)-5\)

Haakjes wegwerken geeft
\(x=32x+36-5\)
\(-31x=31\)
\(x=-1\)

\(\begin{rcases}y=8x+9 \\ x=-1\end{rcases}\begin{matrix}y=8⋅-1+9 \\ y=1\end{matrix}\)

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