system of equations graphically x - 2 y = 3, 3 x

Q) Solve the following system of equations graphically: x – 2 y = 3, 3 x – 8 y = 7.

(Q 32 B – 30/3/3 – CBSE 2026 Question Paper)

Ans:

Step 1: Let’s plot these lines on graph:

First we calculate intersection points on both axes for 1st line: x – 2 y = 3

∵ On x – axis, y = 0, ∴ x = 3, point = (3,0)

∵ On y – axis, x = 0, ∴ y = – $\frac{3}{2}$ , point = (0, – $\frac{3}{2}$ )

Step 2: Next, we calculate intersection points on both axes for 2nd line: 3 x – 8 y = 7

∵ On x – axis, y = 0, ∴ x = $\frac{7}{3}$ , point = ( $\frac{7}{3}$ ,0)

∵ On y – axis, x = 0, ∴ y = – $\frac{7}{8}$ , point = (0, – $\frac{7}{8}$ )

Step 3: Now we plot these point and connect lines.

We can see that both lines are intersecting at point (5,1).

Therefore, point (5,1) is the solution of these lines.

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