Solve the following simultaneous equations using Cramer’s Rule. 5… - Vidyadip

Question

Solve the following simultaneous equations using Cramer’s Rule.
5x + 3y = -11 ; 2x + 4y = -10

✓

Answer

Given equations
$\begin{aligned}
& 5 x+3 y=-11 \\
& 2 x+4 y=-10 \\
& D =\left|\begin{array}{ll}
5 & 3 \\
2 & 4
\end{array}\right| \quad=(5 \times 4)-(2 \times 3)=20-6=14 \\
& D _x=\left|\begin{array}{ll}
-11 & 3 \\
-10 & 4
\end{array}\right|=(-11) \times 4-(-10) \times 3=-44-(-30) \\
& =-44+30=-14 \\
& D_y=\left|\begin{array}{ll}
5 & -11 \\
2 & -10
\end{array}\right|=5 \times(-10)-2 \times(-11)=-50-(-22) \\
& =-50+22=-28 \\
\end{aligned}$
$x=\frac{ D _x}{ D }=\frac{-14}{14}=-1$
and $y=\frac{ D _y}{ D }=\frac{-28}{14}=-2$
$\therefore(x, y)=(-1,-2)$ is the solution.

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