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

x - y = 8, 3x - 3y = 16
x - y - 8 = 0, 3x - 3y -16 = 0
Comparing these equations with
$a_{1}x+b_{1}y+c_1=0$
$a_{2}x+b_{2}y+c_2=0$

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 are parallel to each other and thus have no possible solution.
Hence, the pair of linear equations is inconsistent.