Question

2x+3y=12 ;x-y=1 solve the equations graphically

Answer 1

Answer:

3,2

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Answer 2

Answer:

The vertices of the required triangle -

$A ( 3, 2) , B ( 0, 1 ) , C ( 0,4)$

Step-by-step explanation:

In context to the question asked,

We have to solve the given equation graphically,

As per the data given in the question,

It is given that,

$2x+3y=12$      $...( i)$

$x-y=1$           $...(ii)$

Now, equation ( i ) is written as -

$=> 2x+3y=12$

Shifting 3y on the right side, we get

$=> 2x = 12 - 3y$

$=> x= \frac{12-3y }{2}$           $...(iii)$

( i ) When y = 0,

Now, putting the value of y in the above equation ( iii )

$=> x= \frac{12}{2}$

Divide 12 by 2, we get

( ii ) When y = 2,

Now, putting the value of y in the above equation ( iii )

$=> x= \frac{12-3(2) }{2}$

$=> x= \frac{12-6}{2}$

Subtracting 6 from 12, we get

$=> x= \frac{6}{2}$

Divide 6 by 2, we get

$=> x = 3$

Similarly, we have to solve for equation ( ii )

=> $x-y=1$

Equation ( ii ) is written as,

=> $x=1 +y$     $...( iv)$

( i ) When y = 0,

Now, putting the value of y in the equation ( iv )

=> $x = 1 + 0$

=> $x = 1$

( ii ) When y = -1,

Now, putting the value of y in the equation ( iv )

=> $x = 1 + ( - 1)$

=> $x = 1 - 1$

=> $x = 0$

By using this value we have to draw the graph,

From the graph, we see that,

The 2 lines intersect at points $A ( 3, 2 )$

We also see that the lines are represented by the equation:

$2x + 3y = 12;x - y = 1$

Which meets at points $B ( 0, 1 ) , C ( 0, 4 )$

Hence, The vertices of the required triangle -

$A ( 3, 2) , B ( 0, 1 ) , C ( 0,4)$