Question

check graphically whether the pair of linear equations 4x+6y=96 and 2x+3y=6 is consistent.if so,solve them graphically

Answer 1

Step-by-step explanation:

Given that:

Check graphically whether the pair of linear equations 4x+6y=96 and 2x+3y=6 is consistent.if so,solve them graphically

To find: Solution of linear equations graphically

Solution:

Find at least three points of each line,by putting x and find y

1) 2x+3y=6

Put x=0

$2(0) + 3y = 6 \\ \\ y = 2$

A(0,2)

Put y= 0

$2x + 3(0) = 6 \\ \\ x = 3$

B(3,0)

Put x=-6

$2( - 6) + 3y = 6 \\ \\ 3y = 18 \\ \\ y = 6$

C=(-6,6)

Mark these points and join with a straight line.

Blue line in attached graph.

2) 4x+6y=96

Put x=0

$4(0) + 6y = 96 \\ \\ 6y = 96 \\ \\ y =16$

F(0,16)

Put y= 0

$4x + 6(0) = 96 \\ \\ 4x = 96 \\ \\ x = 24$

E(24,0)

Put x=10

$4(10) + 6y = 96 \\ \\ 6y = 96 - 40 \\ \\ 6y = 56 \\ \\ y = 9.3$

D(10,9.3)

Join Point D,E and F with a straight line.

Green line attached graph.

It is clear from graph that both lines are parallel, thus have no solution.

So, pair of linear equations are inconsistent.

Hope it helps you.