Q1. DETERMINE THE POINT ON THE GRAPH OF THE LINEAR EQUATION ''x+y=6'' WHOSE ORDINATE IS 2 TIMES ITS ABSCISSA.

Q2.HOW MANY SOLUTIONS OF THE EQUATION '' 3x+2=2x-3 ARE THERE ON THE CARTESIAN PLANE?

Q3. DRAW THE GRAPH OF THE LINEAR EQUATIONS-

(i)3x+4y=6

(ii)2x=y+3

1.

The given linear equation is x + y = 6.

x + y = 6

y = 6 – x

When x = 1, y = 6 – 1 = 5

When x = 2, y = 6 – 2 = 4

When x = 3, y = 6 – 3 = 3

These points can be represented in the table as,

The graph of the given linear equation is shown as,

From the graph, we observe that

When x = 2, y = 4

Thus, (2, 4) is the point on the graph whose ordinate is two times its abscissa.

2.

The given is 3x+ 2 = 2x – 3

3x+ 2 = 2x – 3

∴ 3x – 2x = – 3 – 2

x = –5

x = –5 represents a straight parallel to y-axis and passing through (–5, 0) in the Cartesian plane.

All the points lying on the line x = –5 are the solutions of the given equation. Thus, there are infinite solutions of the given equation on the Cartesian plane.

 

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