Determining Nature of Solutions to Linear Equations

• No Solution

• One Solution

• Infinite Solutions

• No Solution

• One Solution

• Infinite Solutions

• No Solution

• One Solution

• Infinite Solutions

• No Solution

• One Solution

• Infinite Solutions

The pair of linear equations 6x-7y = 1 and 3x-4y = 5 has

( 1 mark )

• unique solution

• two solutions

• infinitely many solutions

• no solution

The equations 4x + 3y = 5 and 12x + 9y = 15 represent 

• No  solution

• Infinite many solution

• Unique solution

The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have  

•  a unique solution

• exactly two solutions

• infinitely many solutions

• No solution

Check which of the following options is not the solution of the equation: 7x – 4y = 16

• (0, - 4)

• (16/7, 0)

• (5, 2)

• (2, -1/2)

Answer explanation

7x – 4y = 16 Taking (x = 5, y = 2) L.H.S = 7(5) - 4(2) = 27 ≠ R.H.S Therefore,(5, 2) is not the solution of the equation 7x – 4y = 16 whereas the remaining options are the solutions of this equation. Therefore option 3 is the correct answer.

If a pair of linear equations is consistent, then the lines will be 

•  parallel

• always coincident

• intersecting or coincident

•  always intersecting

Check which of the following options is not the solution of the equation: 2x – y = 6

• (2, 4)

• (3, 0)

• (7/2,1)

• (2, -2)

Answer explanation

2x - y = 6 Taking (x = 2, y = 4) L.H.S = 2(2) - 4 = 0 ≠ R.H.S Therefore, (2, 4) is not the correct solution of the equation 2x - y = 6 Options 2, 3 and 4 are the solutions of the equation 2x - y = 6