Question

Solve the equation: $-4x+8y=12$ and $-2x+4y=6$ and then identify the system of equation.

• A. Consistent
• B. Inconsistent
• C. Dependent
• D. None the above

Answer 1

Answer: (A), (C)

The correct options are
A Consistent
C Dependent

The general form for a pair of linear equations in two variables x and y is

$a_{1}x+b_{1}y+c_1=0$ and

$a_{2}x+b_{2}y+c_2=0$

$-4x+8y=12$ -----------(1)

$-2x+4y=6$ ----------- (2)

Comparing equations 1 and 2 with the general form of equation to write their co-efficient,

$a_1=-4;a_2=-2;b_1=8;b_2=4;c_1=12;c_2=6$

Compare the ratio, $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

$\frac{-4}{-2}=\frac{8}{4}=\frac{12}{6}$

$\therefore$ $2=2=2$

If $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$, then the pair of linear equations has infinitely many solutions.

So, it said to be consistent(dependent).