Optellen geeft \(8x=-4\text{,}\) dus \(x=-\frac{1}{2}\text{.}\)

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

De oplossing is \((x, y)=(-\frac{1}{2}, 3\frac{1}{2})\text{.}\)

\(\begin{cases}a+5b=6 \\ 2a+b=-6\end{cases}\) \(\begin{vmatrix}1 \\ 5\end{vmatrix}\) geeft \(\begin{cases}a+5b=6 \\ 10a+5b=-30\end{cases}\)

Aftrekken geeft \(-9a=36\text{,}\) dus \(a=-4\text{.}\)

\(\begin{rcases}a+5b=6 \\ a=-4\end{rcases}\begin{matrix}-4+5b=6 \\ 5b=10 \\ b=2\end{matrix}\)

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

\(\begin{cases}3x-6y=-3 \\ 4x-5y=5\end{cases}\) \(\begin{vmatrix}5 \\ 6\end{vmatrix}\) geeft \(\begin{cases}15x-30y=-15 \\ 24x-30y=30\end{cases}\)

Aftrekken geeft \(-9x=-45\text{,}\) dus \(x=5\text{.}\)

\(\begin{rcases}3x-6y=-3 \\ x=5\end{rcases}\begin{matrix}3⋅5-6y=-3 \\ -6y=-18 \\ y=3\end{matrix}\)

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

Gelijk stellen geeft \(7x-36=4x-21\)

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

\(\begin{rcases}y=7x-36 \\ x=5\end{rcases}\begin{matrix}y=7⋅5-36 \\ y=-1\end{matrix}\)

De oplossing is \((x, y)=(5, -1)\text{.}\)

Substitutie geeft \(2p+9(4p+3)=-49\)

Haakjes wegwerken geeft
\(2p+36p+27=-49\)
\(38p=-76\)
\(p=-2\)

\(\begin{rcases}q=4p+3 \\ p=-2\end{rcases}\begin{matrix}q=4⋅-2+3 \\ q=-5\end{matrix}\)

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

Substitutie geeft \(a=7(9a+42)-46\)

Haakjes wegwerken geeft
\(a=63a+294-46\)
\(-62a=248\)
\(a=-4\)

\(\begin{rcases}b=9a+42 \\ a=-4\end{rcases}\begin{matrix}b=9⋅-4+42 \\ b=6\end{matrix}\)

De oplossing is \((a, b)=(-4, 6)\text{.}\)