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# 11.8E: Solving Systems with Cramer's Rule (Exercises)

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For the following exercises, find the determinant.

71. $$\left|\begin{array}{cc}100 & 0 \\ 0 & 0\end{array}\right|$$

72. $$\left|\begin{array}{ll}0.2 & -0.6 \\ 0.7 & -1.1\end{array}\right|$$

73. $$\left|\begin{array}{ccc}-1 & 4 & 3 \\ 0 & 2 & 3 \\ 0 & 0 & -3\end{array}\right|$$

74. $$\left|\begin{array}{ccc}\sqrt{2} & 0 & 0 \\ 0 & \sqrt{2} & 0 \\ 0 & 0 & \sqrt{2}\end{array}\right|$$

For the following exercises, use Cramer's Rule to solve the linear systems of equations.

75.

$$4 x-2 y=23$$
$$-5 x-10 y=-35$$

76 .

$$0.2 x-0.1 y=0$$

$$-0.3 x+0.3 y=2.5$$

77 .

$$-0.5 x+0.1 y=0.3$$
$$-0.25 x+0.05 y=0.15$$

78.

$$x+6 y+3 z=4$$

$$2 x+y+2 z=3$$
$$3 x-2 y+z=0$$

79.

$$4 x-3 y+5 z=-\frac{5}{2}$$

$$\quad 7 x-9 y-3 z=\frac{3}{2}$$
$$x-5 y-5 z=\frac{5}{2}$$

80.

$$\frac{3}{10} x-\frac{1}{5} y-\frac{3}{10} z=-\frac{1}{50}$$

$$\frac{1}{10} x-\frac{1}{10} y-\frac{1}{2} z=-\frac{9}{50}$$
$$\frac{2}{5} x-\frac{1}{2} y-\frac{3}{5} z=-\frac{1}{5}$$

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