Aftrekken geeft \(-4a=8\text{,}\) dus \(a=-2\text{.}\)

\(\begin{rcases}a-2b=4 \\ a=-2\end{rcases}\begin{matrix}-2-2b=4 \\ -2b=6 \\ b=-3\end{matrix}\)

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

\(\begin{cases}3x+y=2 \\ 4x-6y=-1\end{cases}\) \(\begin{vmatrix}6 \\ 1\end{vmatrix}\) geeft \(\begin{cases}18x+6y=12 \\ 4x-6y=-1\end{cases}\)

Optellen geeft \(22x=11\text{,}\) dus \(x=\frac{1}{2}\text{.}\)

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

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

\(\begin{cases}4a+6b=-3 \\ 3a+5b=1\end{cases}\) \(\begin{vmatrix}5 \\ 6\end{vmatrix}\) geeft \(\begin{cases}20a+30b=-15 \\ 18a+30b=6\end{cases}\)

Aftrekken geeft \(2a=-21\text{,}\) dus \(a=-10\frac{1}{2}\text{.}\)

\(\begin{rcases}4a+6b=-3 \\ a=-10\frac{1}{2}\end{rcases}\begin{matrix}4⋅-10\frac{1}{2}+6b=-3 \\ 6b=39 \\ b=6\frac{1}{2}\end{matrix}\)

De oplossing is \((a, b)=(-10\frac{1}{2}, 6\frac{1}{2})\text{.}\)

Gelijk stellen geeft \(6y-11=3y-8\)

\(3y=3\) dus \(y=1\)

\(\begin{rcases}x=6y-11 \\ y=1\end{rcases}\begin{matrix}x=6⋅1-11 \\ x=-5\end{matrix}\)

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

Substitutie geeft \(8p+2(6p+12)=4\)

Haakjes wegwerken geeft
\(8p+12p+24=4\)
\(20p=-20\)
\(p=-1\)

\(\begin{rcases}q=6p+12 \\ p=-1\end{rcases}\begin{matrix}q=6⋅-1+12 \\ q=6\end{matrix}\)

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

Substitutie geeft \(y=9(2y-14)+58\)

Haakjes wegwerken geeft
\(y=18y-126+58\)
\(-17y=-68\)
\(y=4\)

\(\begin{rcases}x=2y-14 \\ y=4\end{rcases}\begin{matrix}x=2⋅4-14 \\ x=-6\end{matrix}\)

De oplossing is \((x, y)=(-6, 4)\text{.}\)