Question

x+3y=15 and 2x-3y=-6 find the coordinates with solutions

Answer 1

Answer :

The two lines are

x + 3y = 15 ...(i)
2x - 3y = - 6 ...(ii)

Now, adding (i) and (ii) no. equations, we get

x + 3y + 2x - 3y = 15 - 6

or, 3x = 9

or, x = 9/3

or, x = 3

Now, putting x = 3 in (i), we get

3 + 3y = 15

or, 3y = 15 - 3

or, 3y = 12

or, y = 12/3

or, y = 4

Therefore, the required point of intersection of the two lines are (3, 4).
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NOW, to draw a graph :-

The first line is

x + 3y = 15

or, x/15 + 3y/15 = 1

or, x/15 + y/5 = 1

So, we have two points (15, 0) and (0, 5) to draw the first line.

The second line is

2x - 3y = - 6

or, 2x/(-6) - 3y/(-6) = 1

or, x/(-3) + y/2 = 1

So, we have two points (-3, 0) and (0, 2) to draw the second line.

[N.B. - To draw the 1st line, you can take two points (3, 4) and (0, 5)]
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