Answer:
[tex]\large\boxed{d.\ \text{The solution set is}\ \left(\dfrac{29}{4},\ \dfrac{13}{4}\right)}[/tex]
Step-by-step explanation:
[tex]\left[\begin{array}{ccc}x+3y\\y\end{array}\right] =\left[\begin{array}{ccc}17\\x-4\end{array}\right] \iff\left\{\begin{array}{ccc}x+3y=17&(1)\\y=x-4&(2)\end{array}\right\\\\\\\text{substitute (2) to (1):}\\\\x+3(x-4)=17\qquad\text{use distributive property}\\\\x+(3)(x)+(3)(-4)=17\\\\x+3x-12=17\qquad\text{add 12 to both sides}\\\\4x=29\qquad\text{divie both sides by 4}\\\\\boxed{x=\dfrac{29}{4}}[/tex]
[tex]\text{Put the value of x to (2):}\\\\y=\dfrac{29}{4}-4\\\\y=\dfrac{29}{4}-\dfrac{16}{4}\\\\\boxed{y=\dfrac{13}{4}}[/tex]
