Question

solve graphically
x+2y = 6, 2x-y = 6 ​

Answer 1

Answer:

x+2y=6

or, x= 6-2y. . . . . . (i)

now, 2x-y= 6

or,y= 2x-6. . . . . . (ii)

now, placing y= 2x- 6 in equation (i),

x= 6- 2(2x-6)

or, x= 6- 4x + 12

or, 5x= 18

so, x= 18/5

again placing x= 18/5 in equation (ii),

y= 2(18/5)-6

or,y= 36/5 - 6

or, y= 6/5

so, (x,y)= (18/5, 6/5)

hope it helps

Answer 2

$\sf\huge \mathbb{\underline{\underline{{Solution}}}}$We have given two pair of linear equations and we have to find the value of x and y through graph.

For that firstly convert the Equation either in the form of x or y and then plot points into and obtained the coordinate . Put the coordinate into graph of both the Equation and we obtained a interesting point with the help of coordinate of both the Equation which will be our final solution.

$\sf \bold{x + 2y = 6} - - - - (1)$

$\sf \bold{2x - y = 6} - - - - (2)$

Solving equation 1

$\sf \boxed{ \bold{ \red{x = 6 - 2y}}}$

$\sf \: at \: y = 3$

$\sf \implies \: x = 6$

$\sf \: at \: y = 0$

$\sf \implies \: x = 6$

Now,we obtained the coordinates (0,3)&(6,0).

Next step is to plot these coordinates into the graph.

$\sf \boxed{ \bold {\blue{x = \dfrac{6 + y}{2} }}}$

$\sf \: at \: y = 0$

$\sf \implies \: x = \dfrac{6}{2} = 3$

$\sf \: at \: y = - 6$

$\sf \implies \: x = 0$

We obtained the coordinates (3,0)&(0,-6).Now,plot these coordinates into the graph.

After plotting the coordinates of both the Equation we obtained a straight line graph which intersect at the points (3.6,1.2).

Therefore,the solution of the given Equation is :x=3.6 & y= 1.2.

Check:-

$\sf \implies \: x + 2y = 6$

Taking LHS

$\sf \implies3 .6 + 2(1.2)$

$\sf \implies3.6 + 2.4$

$\sf = 6$

∵LHS=RHS(Verified)