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

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

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

\(\begin{cases}x+3y=5 \\ 2x+2y=4\end{cases}\) \(\begin{vmatrix}2 \\ 1\end{vmatrix}\) geeft \(\begin{cases}2x+6y=10 \\ 2x+2y=4\end{cases}\)

Aftrekken geeft \(4y=6\text{,}\) dus \(y=1\frac{1}{2}\text{.}\)

\(\begin{rcases}x+3y=5 \\ y=1\frac{1}{2}\end{rcases}\begin{matrix}x+3⋅1\frac{1}{2}=5 \\ x=\frac{1}{2}\end{matrix}\)

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

\(\begin{cases}2p-2q=-4 \\ 5p+3q=2\end{cases}\) \(\begin{vmatrix}3 \\ 2\end{vmatrix}\) geeft \(\begin{cases}6p-6q=-12 \\ 10p+6q=4\end{cases}\)

Optellen geeft \(16p=-8\text{,}\) dus \(p=-\frac{1}{2}\text{.}\)

\(\begin{rcases}2p-2q=-4 \\ p=-\frac{1}{2}\end{rcases}\begin{matrix}2⋅-\frac{1}{2}-2q=-4 \\ -2q=-3 \\ q=1\frac{1}{2}\end{matrix}\)

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

Gelijk stellen geeft \(5x-29=2x-14\)

\(3x=15\) dus \(x=5\)

\(\begin{rcases}y=5x-29 \\ x=5\end{rcases}\begin{matrix}y=5⋅5-29 \\ y=-4\end{matrix}\)

De oplossing is \((x, y)=(5, -4)\text{.}\)

Substitutie geeft \(4(9y-24)+2y=-20\)

Haakjes wegwerken geeft
\(36y-96+2y=-20\)
\(38y=76\)
\(y=2\)

\(\begin{rcases}x=9y-24 \\ y=2\end{rcases}\begin{matrix}x=9⋅2-24 \\ x=-6\end{matrix}\)

De oplossing is \((x, y)=(-6, 2)\text{.}\)

Substitutie geeft \(b=6(8b+15)+4\)

Haakjes wegwerken geeft
\(b=48b+90+4\)
\(-47b=94\)
\(b=-2\)

\(\begin{rcases}a=8b+15 \\ b=-2\end{rcases}\begin{matrix}a=8⋅-2+15 \\ a=-1\end{matrix}\)

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