Q) Solve the following system of linear equations graphically:

2x- y – 2= 0

– 4 x + y + 4 = 0

Also, find the absolute difference between the ordinates of the points where given lines cut y – axis.

PYQ: 28 – CBSE 2025 – Code 30 – Series 5 – Set 1

Ans:

Part 1: Solving the linear equations:

Step 1: To plot the equations, let’s first find out the coordinates of points lying on these lines:

For line: 2 x – y – 2 = 0, we calculate coordinates of various points:

at X = 0, 2 (0) – y – 2 = 0  ∴ y = – 2

at X = 1,  2 (1) – y – 2 = 0 ∴ y = 0

at X = 2,  2 (2) – y – 2 = 0 ∴ y = 2

at X = 3,  2 (3) – y – 2 = 0 ∴ y = 4

Hence, we get the following table:

Step 2: Similarly, for line: – 4 x + y + 4 = 0, we calculate coordinates of various points:

at X = 0, – 4 (0) + y + 4 = 0 ∴ y = – 4

at X = 1, – 4 (1) + y + 4 = 0 ∴ y = 0

at X = 2, – 4 (2) + y + 4 = 0 ∴ y = 4

at X = 3, – 4 (3) + y + 4 = 0 ∴ y = 8

Hence, we get the following table:

Step 3: Now let’s plot both of these lines connecting each of the points:

From the diagram, we can see that the lines intersect each other at point (1, 0)

Therefore, the solution of the lines is (1, 0).

[Note: Let’s check our answer: At (1, 0), LHS value of (2 x – y – 2 = 0) is  2(1) – (0) – 2 = 2 – 2 = 0 = RHS

at (1, 0), LHS value of (- 4 x + y + 4 = 0) is – 4 (1) + (0) + 4 = – 4 + 4 = 0 = RHS

Since RHS values are same as LHS for both equations at (1, 0), hence our answer is correct.]

Part 2: Absolute difference between ordinate values:

Step 4: When a line cuts Y – axis, its abscissa values are zero

We can see in step1, line 2 x – y – 2 = 0, cuts Y-axis at (0, – 2), hence its ordinate value is – 2

and line cuts Y-axis at (0, – 4), hence its ordinate value is – 4

∴ The difference between these 2 ordinate values = – 4 – (- 2) = – 2

Since we need to find absolute difference, hence sign value will be dropped

Therefore, the absolute difference between the ordinates of the two points is 2.

[Note: the absolute difference will be like distance between 2 points]

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