Question

if dx=-35 and d=-5are the values of the determinants for certain simultaneous equations in x and y, find x​

Answer 1

Appropriate Question :-

if dx=-35 and d=-5are the values of the determinants for certain simultaneous equations in x.

Solution :-

Given :

• dx = -35
• d = -5

Need to find :

• x

Using formula :

$\sf:\longmapsto{x = \frac{dx}{d} }$

Now,

$\sf:\longmapsto{x = \frac{ - 35}{ - 5} } \\ \\ \bf:\longmapsto \red{x = 7} \: \: \:$

Additional Information :-

Let assume,

• ax + by = e
• cx + dy = f

are the equation then,

D =

$\sf:\longmapsto{ D = \begin{gathered} \begin{gathered} \begin{gathered}\begin{gathered}\left|\begin{array}{cc} \sf a & \sf b \\ \sf c & \sf d \end{array}\right| </p><p> \end{gathered} \end{gathered} \end{gathered}\end{gathered}}$

Dx =

$\sf:\longmapsto{ Dx = \begin{gathered} \begin{gathered} \begin{gathered}\begin{gathered}\left|\begin{array}{cc} \sf e & \sf b \\ \sf f & \sf d \end{array}\right| </p><p> \end{gathered} \end{gathered} \end{gathered}\end{gathered}}$

Dy =

$\sf:\longmapsto{ Dy= \begin{gathered} \begin{gathered} \begin{gathered}\begin{gathered}\left|\begin{array}{cc} \sf a & \sf e \\ \sf c & \sf f \end{array}\right| </p><p> \end{gathered} \end{gathered} \end{gathered}\end{gathered}}$

x =

$\sf:\longmapsto{x = \frac{Dx}{D}}</p><p>$

y =

$\sf:\longmapsto{y = \frac{Dy}{D}}</p><p>$

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