Question

Determine how many solution exist for the following pair of equations $8x+5y=9,16x+10y=27$

• A. Both equations form coincident line hence they have no solutions.
• B. Both equations form parallel lines hence they have no solutions.
• C. Both equations form intersecting lines hence they have no solutions.
• D. None of these

Answer 1

The correct option is B Both equations form parallel lines hence they have no solutions.

The following pair of equations can be written as

$8x+5y-9=0;16x+10y-27=0;$

Here $\frac{a_1}{a_2}=\frac{8}{16}=\frac{1}{2}$

$\frac{b_1}{b_2}=\frac{5}{10}=\frac{1}{2}$

$\frac{c_1}{c_2}=\frac{-9}{-27}=\frac{1}{3}$,

We can see $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

Hence, the given pair of the linear equation is inconsistent and has no solution.

For a graphical solution,

$8x+5y=9$

$y=\frac{9-8x}{5}$

$16x+10y=27$

$y=\frac{27-16x}{10}$

Now, we can make the table and make the graph as shown in the solution.