The solution of equations $x + y = 10$,$2x + y = 18$,and $4x - 3y = 26$ is:

Let $a, \lambda, \mu \in \mathbb{R}$. Consider the system of linear equations:
$a x + 2 y = \lambda$
$3 x - 2 y = \mu$
Which of the following statement$(s)$ is(are) correct?
$(A)$ If $a = -3$,then the system has infinitely many solutions for all values of $\lambda$ and $\mu$.
$(B)$ If $a \neq -3$,then the system has a unique solution for all values of $\lambda$ and $\mu$.
$(C)$ If $\lambda + \mu = 0$,then the system has infinitely many solutions for $a = -3$.
$(D)$ If $\lambda + \mu \neq 0$,then the system has no solution for $a = -3$.

If ${a_1}x + {b_1}y + {c_1}z = 0, {a_2}x + {b_2}y + {c_2}z = 0, {a_3}x + {b_3}y + {c_3}z = 0$ and $\left| \begin{matrix} {a_1} & {b_1} & {c_1} \\ {a_2} & {b_2} & {c_2} \\ {a_3} & {b_3} & {c_3} \end{matrix} \right| = 0$,then the given system has

If $A$ is a matrix such that $\left[\begin{array}{ll} 2 & 1 \\ 3 & 2 \end{array}\right] A \left[\begin{array}{l} 1 \\ 1 \end{array}\right] = \left[\begin{array}{l} 1 \\ 0 \end{array}\right]$,then $A$ is equal to

If the set of equations $x+2y+3z=6$,$x+3y+5z=9$,and $2x+5y+az=b$ has a unique solution,then:

Consider the system of linear equations $a_1x + b_1y + c_1z + d_1 = 0$,$a_2x + b_2y + c_2z + d_2 = 0$ and $a_3x + b_3y + c_3z + d_3 = 0$. Let us denote by $\Delta (a,b,c)$ the determinant $\begin{vmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{vmatrix}$. If $\Delta (a,b,c) \neq 0$,then the value of $x$ in the unique solution of the above equations is: