Question

Check whether the following pair of equations is consistent. Verify by a graphical representation. 3x + 4y = 2
6x + 8y = 4.

Answer 1

Given , pair of equations are :
3x + 4y = 2
(x = 0, y = 1/2 ) , (x = 1, y =-1/4 ) , (x = -2 , y = 2)
6x + 8y = 4
(x = 0, y = 1/2) , (x = 1, y = -1/4) , (x = -2, y = 2)

Here, $a_1=3,b_1=4,c_1=2$
and $a_2=6,b_2=8,c_2=4$
$\therefore\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}=\frac{1}{2}$

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
therefore two given lines are inconsistent.

Answer 2

Answer:

Step-by-step explanation:Let the lengths and breadth of rectangle be l & b respectively.

Now l = b+5, perimeter = 2(l+b) = 58 cm

2(b +b +5) = 58

2b + 5 = 29

2b = 24

b = 12 and length = b +5 = 17