Question

Find a and b if the points P(3, 0) and $\mathrm{Q}\left(2,\frac{4}{3}\right)$ lie on the graph ax + by = 12

Answer 1

$$\begin{gathered} \mathrm{Given}:\mathrm{Points}\left(3,0\right)\mathrm{and}\left(2,\frac{4}{3}\right)\mathrm{lie}\mathrm{on}\mathrm{the}\mathrm{graph}\mathrm{of}ax+by=12. \\ \mathrm{Therefore},\mathrm{these}\mathrm{two}\mathrm{points}\mathrm{will}\mathrm{satisfy}\mathrm{the}\mathrm{equation}. \\ \mathrm{So}, \\ a\times 3+b\times 0=12 \\ \Rightarrow 3a+0=12 \\ \Rightarrow 3a=12 \\ \Rightarrow a=4 \\ \mathrm{And} \\ a\times 2+b\times \frac{4}{3}=12 \\ \Rightarrow 6a+4b=36 \\ \Rightarrow 3a+2b=18 \\ \mathrm{Using}a=4\text{in the equation, we get:} \\ 3\times 4+2b=18 \\ \Rightarrow 12+2b=18 \\ \Rightarrow 2b=6 \\ \Rightarrow b=3 \\ \therefore a=4\mathrm{and}b=3. \end{gathered}$$