Problem Sheet class 7 part 2

Problem Sheet class 7 part 2 - Transcript

Maths Problem sheet 2
Solve the simultaneous equations by graphical means stating the solution
y 3 x y 1 x for values of x between 5 and 5
y 1 x y 3 2x for values of x between 0 and 10
y 2 0 5x y 3 2x for values of x between 3 and 5
2x y 11 5x y 8 for values of x between 2 and 4
y 5 4x y 3 2x for values of x between 3 and 3
4y 6 x y 3 x for values of x between 0 and 8
2y 4 3x y 2 1 5x for values of x between 0 and 9
y 3 2x x 0 5y 1 5 0 for values of x between 0 and 6
Solve the following simultaneous equations by algebraic means
x y 10 x y 6
3x 2y 14 2x 5y 3
y 17 3x y 8 2x
y 4 x 2y 22 4x
2p 7q 1 5p 2q 17
3m 5n 18 2m 3n 7
y 0 75x 2 y 1 5x 2 5
Solve the following simultaneous equations algebraically by equating or substituting do not use the elimination method
y 1 5x 3x 4y 18
3x 2y 6
y 5x 2 2x y 5
x 3y 5 4x 2y 8
3m 2p 9
y 5x 4 y 8x 9
y 0 5x 2 y 2x 6
3x y 5 5x 2y 9
11x 2y 37 12x y 34
2x 4y 14 3x 2y 1 5
2x 5y 7 3x 2 5y 2
3x 2y 10 4 5x 3y 15 0
5x 2y 11 10x 4y 5
How do you know by simple inspection that there is no solution to this pair of equations
y 12 4x y 5 4x
Rearrange one of the equations to help you explain why there are infinitely many solutions
y 12 2 0 5x x 2y 24 4 0
Answers to Maths Problem Sheet 2
1 y 3 x
x 5 2 2 5
y 8 5 1 2

y 1 x
x 5 2 2 5
y 6 3 1 4

The solution is x 2 y 1

2
y 1 x
x 0 3 7 10
y 1 4 8 11

y 3 2x
x 0 3 7 10
y 3 3 11 17


The solution is x 4 y 5
3 y 2 0 5x
x 3 1 2 5
y 3 2 5 1 0 5

y 3 2x
x 3 1 2 5
y 9 5 1 7

The solution is x 2 y 1
4 2x y 11
x 2 0 2 4
y 7 11 15 19

5x y 8
x 2 0 2 4
y 2 8 18 28

The solution is x 1 y 13 although you can only estimate this from the graph
5 y 5 4x
x 3 1 1 3
y 7 1 9 17

y 3 2x
x 3 1 1 3
y 9 5 1 3

this can only be estimated from the graph
6 4y 6 x
x 0 3 5 8
y 1 5 0 75 0 25 0 5

y 3 x
x 0 3 5 8
y 3 0 2 5

The solution is x 3 6 y 0 6 only an approximate answer can be read from the graph
7 2y 4 3x
x 0 3 6 9
y 2 6 5 11 15 5

y 2 1 5x
x 0 3 6 9
y 2 2 5 7 11 5

There is no solution the lines are parallel and will never meet Their slopes are the same
8 y 3 2x
x 0 2 4 6
y 3 7 11 15

x 0 5y 1 5 0
x 0 2 4 6
y 3 7 11 15

There are infinitely many solutions as the lines are coincident
x 8 y 2
x 4 y 1
x 5 y 2
x 5 y 1
p 3 q 1
m 1 n 3
x 2 y 0 5
x 2 y 3
x 4 y 3
x 1 y 3
x 1 y 2
m 1 p 3
x 1 y 1

x 1 y 2
x 3 y 2
x 1 5 y 3

Infinitely many solutions the equations are not independent
No solutions
The graphs of the two equations are parallel both with a slope of 4 Parallel lines never cross so there is no solution
The first equation may be rearranged to give x 2y 24 4 0 ie the same as second equation The two equations are not independent
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