Question

Solve the simultaneous equation 5x+3y=-11 x+2y=-5 using Cramer's rule.

Answer 1

The solution of given system of equations is (-1,-2).

Step-by-step explanation:

If a system of equations is

$ax+by=e$

$cx+dy=f$

then by Cramer's rule

$x=\dfrac{D_x}{D} and y=\dfrac{D_y}{D}$

where,

$D_x=\left|\begin{array}{cc}e&b\\f&d\end{array}\right|$

$D_y=\left|\begin{array}{cc}a&e\\c&f\end{array}\right|$

$D=\left|\begin{array}{cc}a&b\\c&d\end{array}\right|$

The given system of equations is

$5x+3y=-11$

$x+2y=-5$

Here, a=5, b=3, c=1, d=2, e=-11, f=-5.

Using Cramer's rule

$D=\left|\begin{array}{cc}5&3\\1&2\end{array}\right|=10-3=7$

$D_x=\left|\begin{array}{cc}-11&3\\-5&2\end{array}\right|=-22-(15)=-7$

$D_y=\left|\begin{array}{cc}5&-11\\1&-5\end{array}\right|=-25-(-11)=-14$

$x=\dfrac{-7}{7}=-1$

$y=\dfrac{-14}{7}=-2$

Therefore, the solution of given system of equations is (-1,-2).

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Solve the following simultaneous equations using cramer's rule. 5x+3y=-11 ; 2x + 4y=-10​

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Answer 2

The values of x and y to the given equations is x=-1 and y=-2

Therefore the solution is (-1,-2)

Step-by-step explanation:

• Given equations are $5x+3y=-11\hfill (1)$

and $x+2y=-5\hfill (2)$

• To find the solution to the given simultaneous equation by Cramer's rule :
• First find the determinant of the given equations

• D=$\left|\begin{array}{cc}5&3\\1&2\end{array}\right|$

=10-3

=7

• Therefore D=7

• $D_x=\left|\begin{array}{cc}-11&3\\ -5&2\end{array}\right|$

$=-22+15$

=-7

• Therefore $D_x=-7$

• $D_y=\left|\begin{array}{cc}5&-11\\ 1&-5\end{array}\right|$

=-25+11

=-14

• Therefore $D_y=-14$
• Now we have by Cramer's rule

• $x=\frac{D_x}{D}$

$x=\frac{-7}{7}$

• Therefore x=-1
• $y=\frac{D_y}{D}$

$y=\frac{-14}{7}$

• Therefore y=-2
• The solution is (-1,-2)

• The values of x and y to the given equations is x=-1 and y=-2