Question

Question 4 (ii)
Which of the following pairs of linear equations are consistent/ inconsistent? If consistent, obtain the solution graphically:
x - y = 8, 3x - 3y = 16

Answer 1

The given equations are x - y = 8 and 3x - 3y = 16
They can be written as x - y - 8 = 0 and 3x - 3y -16 = 0

Comparing these equations with $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$, we get:

$a_1=1,b_1=-1,and{c}_1=-8$
$a_2=3,b_2=-3and{c}_2=-16$

$\frac{a_1}{a_2}=\frac{1}{3}$
$\frac{b_1}{b_2}=\frac{-1}{-3}=\frac{1}{3}$ and
$\frac{c_1}{c_2}=\frac{8}{16}=\frac{1}{2}$

Hence, $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

Therefore, these linear equations represent parallel lines and thus have no possible solution.
Hence, the pair of linear equations is inconsistent.