Answer to Question #177279 in Math for John

Question

(12) Solve the pair of simultaneous equations below:-

4a − 3b = 18

a + 2b = -1

(13) The molar heat capacity of a solid compound is given by c = a + bt

Given that when and that when c = 10 when t = 50 and that c = 13 when t = 80 Find the values of a and b.

(ALL WORKING OUTS TO BE SHOWN)

Answer 1

(12)

$\begin{matrix} 4a-3b=18 \\ a + 2b = -1 \end{matrix}$

$\begin{matrix} 4a-3b-4a-8b=18-(-4) \\ a = -1-2b \end{matrix}$

$\begin{matrix} -11b=22 \\ a = -1-2b \end{matrix}$

$\begin{matrix} a=3 \\ b = -2 \end{matrix}$

(13)

$\begin{matrix} a+50b=10 \\ a + 80b = 13 \end{matrix}$

$\begin{matrix} a+80b-a-50b=13-10 \\ a = 10-50b \end{matrix}$

$\begin{matrix} 30b=3 \\ a =10-50b \end{matrix}$

$\begin{matrix} a=5 \\ b = 0.1 \end{matrix}$