Stelsels oplossen

Aftrekken geeft \(-a=2\text{,}\) 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 \((a, b)=(-2, -3)\text{.}\)

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

Aftrekken geeft \(-8y=-16\text{,}\) dus \(y=2\text{.}\)

\(\begin{rcases}2x-6y=-6 \\ y=2\end{rcases}\begin{matrix}2x-6⋅2=-6 \\ 2x=6 \\ x=3\end{matrix}\)

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

\(\begin{cases}3a-3b=-6 \\ 2a+4b=-1\end{cases}\) \(\begin{vmatrix}4 \\ 3\end{vmatrix}\) geeft \(\begin{cases}12a-12b=-24 \\ 6a+12b=-3\end{cases}\)

Optellen geeft \(18a=-27\text{,}\) dus \(a=-1\frac{1}{2}\text{.}\)

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

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

Gelijk stellen geeft \(8x+36=4x+16\)

\(4x=-20\) dus \(x=-5\)

\(\begin{rcases}y=8x+36 \\ x=-5\end{rcases}\begin{matrix}y=8⋅-5+36 \\ y=-4\end{matrix}\)

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

Substitutie geeft \(6x+9(4x-7)=21\)

Haakjes wegwerken geeft
\(6x+36x-63=21\)
\(42x=84\)
\(x=2\)

\(\begin{rcases}y=4x-7 \\ x=2\end{rcases}\begin{matrix}y=4⋅2-7 \\ y=1\end{matrix}\)

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

Substitutie geeft \(q=6(3q-11)-19\)

Haakjes wegwerken geeft
\(q=18q-66-19\)
\(-17q=-85\)
\(q=5\)

\(\begin{rcases}p=3q-11 \\ q=5\end{rcases}\begin{matrix}p=3⋅5-11 \\ p=4\end{matrix}\)

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