Important Math Questions: Linear Equations in two Variables (Graphs)

Q1. Solve graphically the following system of equations:

a) x + y = 4, 2x – 3y = 3
[x = 3, y = 1]

b) 5x – y – 7 = 0, x – y + 1 = 0
[x = 2, y = 3]

c) 3x + y + 1 = 0, 2x – 3y + 8 = 0
[x = -1, y = 2]

Q2. Show graphically that each of the following systems of equations is INCONSISTENT (i.e. has NO SOLUTION)

a) 2x + 3y = 6, 4x + 6y = 24

b) 2 y – x = 9, 6 y – 3x = 21

Q3. Show graphically that each of the following systems of equations has INFINITE no. of solutions:

a) 2y = 4x – 6, 2x = y + 3

b) x + y = 3, 2x = 6 – 2y

Q4. Solve the following system of linear equations graphically:

2x – y = -8; 8x + 3y = 24

Determine the vertices of the triangle formed by the lines representing these equations and the x – axis. Shade the triangular region so formed.

[x = 0, y = 8; (0, 8), (-4, 0), (3, 0)]

Q5. Draw graphs of the following equations on the same graph paper:

2x + 3y = 12, x – y = 1

Find the co-ordinates of the vertices of the triangle formed by the two straight lines and the y-axis.

[(0, -1), (3, 2), (0, 4)]

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