Practice the questions given in the worksheet on graphing simultaneous equations. The questions are based on graphing linear equations on co-ordinate graph. When we draw two simultaneous linear equations on the plane, there are three possible results:
(i) The graph lines intersect just once then we get unique solution.
(ii) The graph lines never touch each other then we get no solution.
(iii) The graph lines lie on top of each other then we get infinite solution.
1. Draw the graph of the following simultaneous linear equations and solve them graphically.
(i) x + y = 5 and x – y = 1
(ii) x + y = 0 and 2x – y = 9
(iii) 3x -4y = 15 and 5x -2y = 11
(iv) 3x – y = 2 and 2x – y = 3
(v) 2x – 3y = 4 and 3y – x = 4
(vi) 2x – 3y = -9 and 6x + 18 = 9y
(vii) x + 3y = 4 and 3x – y = 2
(viii) 5x – y = 3 and 2x + y = 5
(ix) x + y + 3 = 0 and x + 3y – 1 = 0
(x) x = y + 6 and y = 2x – 3
(xi) x = y and x = -y
(xii) x + y = 4 and 2x – y = 2
2. (a) Solve the following system of linear equations graphically 2x + y -5 = 0 and x + y -3 = 0.
(b) Also find the points where the graph lines meet the y-axis.
3. Show graphically that the simultaneous equations 2x + y = 6 and 6x + 3y = 18 has infinitely many solutions.
4. Show graphically that the simultaneous equations 2x + 3y = 4 and 4x + 6y = 12 is inconsistent.
5. Show graphically that the simultaneous linear equations x - 2y = 2 and 4x - 2y = 5 is consistent.
Answers for the worksheet on simultaneous equations are given below to check the exact answers of the above questions using graphs to solve systems of equations.
1. (i) x = 3 and y = 2
(ii) x = 3 and y = -3
(iii) x = -1 and y = 3
(iv) x = - 1 and y = -5
(v) x = 8 and y = 4
(vi) No solutions, since both lines are parallel
(vii) x = 1 and y = 1
(viii) x = 2 and y = 1
(ix) x = -5 and y = 2
(x) x = -3 and y = -9
(xi) x = 0 and y = 0
(xii) x = 2 and y = 2
2. (a) x = 2 and y = 1.
(b) (0, 5) and (0, 3)
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