(i) Use the graph shown to fi nd the point of intersection P of the lines 3x + 4y = 23 and 2x + y = 12
(ii) Verify your answer to (i) by solving the equations simultaneously.
Solution (ii)
y
4 3 2 1
–1 0 –1
2x + y = 12 3x + 4y = 23 P 1 2 3 4 5 6 x
Practice questions 31.7
1. Find the point of intersection of each of the pairs of lines shown below. (i)
y
3 2 1
–3 –2 –1 0 –1
1 2 3 x (ii) –3 –2 –1
–2 –1
–3 –4 –3 –2 y
1 0
1 2 3 x (iii) y
3 4
2 1
–1 0 –1
1
2. Find the point of intersection of each of the following pairs of lines by graphing each pair using the same axes and scales.
(i) x + y = 3 and 2x + y = 5 (ii) 2x + y = 6 and 2x + 3y = 10
(iii) 3x − 4y = 0 and 2x − 3y = 0 (iv) x + y = 5 and 2x − y = 1
(iii) 3x + 2y = 7 and 4x − y = 13 (iv) 6x − 5y = 29 and 5x + 4y = 16
(v) x − y = − 3 and x + 2y = 9 (vi) 5x + 2y = 24 and 3x − y = 10
3. Use simultaneous equations to fi nd the point of intersection of the following pairs of lines. (i) x − 3y = 1 and 4x + 3y = 34 (ii) 2y = − x + 4 and 2x = y + 3
4. The diagram shows two straight lines intersecting at point A. The equations of the lines are: y = 3x − 4 y = 2x − 3 Work out the coordinates of A.
506 Linking Thinking 1 y y = 3x – 4 y = 2x – 3 x A
(v) x + y − 2 = 0 and − y = − 3x + 6 (vi) 2x = 3y + 13 and x − 4y − 9 = 0