8.4 Cramer’s rule

Use Cramer’s rule to solve the equations systems [math]\begin{cases}5x+6y=20\\4x-7y=-55\end{cases}[/math] (Solve for [math]x[/math] only)

(Calculator) Use Cramer’s rule to solve the equations systems[math]\begin{cases}x+2y+5z=7\\4x-3y-z=2\\3x+4z=5\end{cases}[/math] (Solve for [math]y[/math] only)

(Calculator) How many solutions does the equations system [math]\begin{cases}x+y+z=0\\x+y-2z=0\\x+y+2z=3\end{cases}[/math] have?

If [math]x=-3, y=4[/math] is the solution to the equations system [math]\begin{cases}ax+by=c\\dx+ey=f\end{cases}[/math], what is the solution to the equation system [math]\begin{cases}ax-2by=3c\\dx-2ey=3f\end{cases}[/math]?

Find the constant [math]a[/math] such that the equations system [math]\begin{cases}(1-a)x+y+z=1\\x+(1-a)y+z=1\\x+y+(1-a)z=1\end{cases}[/math] has no solutions.

Use Cramer’s rule to solve [math]\begin{cases}4x+3y=18\\3x+4y=17\end{cases}[/math]

Use Cramer’s rule to solve [math]\begin{cases}9x+y+2z=3\\8x+2y+3z=5\\-x+3y+z=4\end{cases}[/math]. (Solve [math]y[/math] only)