Question

Pair of linear equation are consistent or inconsistent.
4x-5y-12=0, 10y+20=8x

Answer 1

Answer:

a1=4 b1=-5 c1=-12

a2=-8 b2=20 c2=20

a1/a2 is not equal to b1/b2

-1/2 is not equal to -1/4

pair of linear equations are consistent

Answer 2

Answer:

The Pair of linear equation are inconsistent.

Step-by-step explanation:

We can determine if a pair of linear equation is consistent or not using the ratios of the coefficient of x, y as well as the constants.

The given equations is;

4x-5y-12=0

10y+20=8x or 8x - 10y - 20 = 0.

Here, $a_{1}$ = 4 ; $b_{1}$ = -5 ; $c_{1}$ = -12.

         $a_{2}$ = 8 ; $b_{2}$ = -10 ; $c_{2}$ = -20

Now,

$\frac{a_{1}}{a_{2}} = \frac{4}{8} = \frac{1}{2}$

$\frac{b_{1}}{b_{2}} = \frac{-5}{-10} = \frac{1}{2}$

$\frac{c_{1}}{c_{2}} = \frac{-12}{-20} = \frac{3}{5}$

As, $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$, the given pair of linear equations are inconsistent.

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