Optellen geeft \(5a=-10\text{,}\) dus \(a=-2\text{.}\)

\(\begin{rcases}a+6b=-5 \\ a=-2\end{rcases}\begin{matrix}-2+6b=-5 \\ 6b=-3 \\ b=-\frac{1}{2}\end{matrix}\)

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

\(\begin{cases}4a+2b=-1 \\ 3a+b=-4\end{cases}\) \(\begin{vmatrix}1 \\ 2\end{vmatrix}\) geeft \(\begin{cases}4a+2b=-1 \\ 6a+2b=-8\end{cases}\)

Aftrekken geeft \(-2a=7\text{,}\) dus \(a=-3\frac{1}{2}\text{.}\)

\(\begin{rcases}4a+2b=-1 \\ a=-3\frac{1}{2}\end{rcases}\begin{matrix}4⋅-3\frac{1}{2}+2b=-1 \\ 2b=13 \\ b=6\frac{1}{2}\end{matrix}\)

De oplossing is \((a, b)=(-3\frac{1}{2}, 6\frac{1}{2})\text{.}\)

\(\begin{cases}5x-4y=6 \\ 4x-3y=6\end{cases}\) \(\begin{vmatrix}3 \\ 4\end{vmatrix}\) geeft \(\begin{cases}15x-12y=18 \\ 16x-12y=24\end{cases}\)

Aftrekken geeft \(-x=-6\text{,}\) dus \(x=6\text{.}\)

\(\begin{rcases}5x-4y=6 \\ x=6\end{rcases}\begin{matrix}5⋅6-4y=6 \\ -4y=-24 \\ y=6\end{matrix}\)

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

Gelijk stellen geeft \(7x+3=4x\)

\(3x=-3\) dus \(x=-1\)

\(\begin{rcases}y=7x+3 \\ x=-1\end{rcases}\begin{matrix}y=7⋅-1+3 \\ y=-4\end{matrix}\)

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

Substitutie geeft \(3p+2(7p+24)=-3\)

Haakjes wegwerken geeft
\(3p+14p+48=-3\)
\(17p=-51\)
\(p=-3\)

\(\begin{rcases}q=7p+24 \\ p=-3\end{rcases}\begin{matrix}q=7⋅-3+24 \\ q=3\end{matrix}\)

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

Substitutie geeft \(x=5(7x+27)+1\)

Haakjes wegwerken geeft
\(x=35x+135+1\)
\(-34x=136\)
\(x=-4\)

\(\begin{rcases}y=7x+27 \\ x=-4\end{rcases}\begin{matrix}y=7⋅-4+27 \\ y=-1\end{matrix}\)

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