Question
Solve the following simultaneous equations$:13a - 11b = 70,11a - 13b = 74$
✓
Answer
The given equation are
$13a - 11b = 70\dots ....(i)$
$11a - 13b = 74 \dots....(ii)$
Multiplying eqn. $(i)$ by $13$ and eqn. $(ii)$ by $4$, we get
$169a - 143b = 910 \dots....(iii)$
$121a - 143b = 814\dots ....(iv)$
Subtracting eqn. $(iv)$ from eq. $(iii),$ we get
$48a = 96$
$\Rightarrow a = 2$
Subtracting the value of $a$ in eqn. $(i),$ we get
$13(2) - 11b = 70$
$\Rightarrow 26 - 11b = 70$
$\Rightarrow -11b = 70 - 26$
$\Rightarrow -11b = 44$
$\Rightarrow b = -4$
Thus, the solution set is $(2, - 4).$
$13a - 11b = 70\dots ....(i)$
$11a - 13b = 74 \dots....(ii)$
Multiplying eqn. $(i)$ by $13$ and eqn. $(ii)$ by $4$, we get
$169a - 143b = 910 \dots....(iii)$
$121a - 143b = 814\dots ....(iv)$
Subtracting eqn. $(iv)$ from eq. $(iii),$ we get
$48a = 96$
$\Rightarrow a = 2$
Subtracting the value of $a$ in eqn. $(i),$ we get
$13(2) - 11b = 70$
$\Rightarrow 26 - 11b = 70$
$\Rightarrow -11b = 70 - 26$
$\Rightarrow -11b = 44$
$\Rightarrow b = -4$
Thus, the solution set is $(2, - 4).$
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