Everything Maths Grade 10

4.Solve forxandy:

a)  10 x= 1 and 4 x+ 10y= 9. b) 3 x 14 y= 0andx 4 y+ 1 = 0

c) x+y= 8and 3 x+ 2y= 21 d)y= 2x+ 1andx+ 2y+ 3 = 0

e) 5 x 4 y= 69and 2 x+ 3y= 23 f)x+ 3y= 26and 5 x+ 4y= 75

g) 3 x 4 y= 19and 2 x 8 y= 2 h)

a

2

+b= 4and

a

4

b

4

= 1

i) 10 x+y= 1 and 10 x 2 y= 5 j) 10 x 10 y= 2 and 2 x+ 3y= 2

k)

1

x

+

1

y

= 3and

1

x

1

y

= 11 l)y=

2(x^2 + 2) 3

x^2 + 2

andy= 2

3

x^2 + 2

m) 3 a+b=

6

2 a

and 3 a^2 = 3ab

5.Solve graphically and check your answer algebraically:

a) y+ 2x= 0andy 2 x4 = 0 b)x+ 2y= 1and

x

3

+

y

2

= 1

c) y2 = 6xandyx= 3 d) 2 x+y= 5and 3 x 2 y= 4

e) 5 =x+yandx=y 2

For more exercises, visit http://www.everythingmaths.co.za and click on ’Practise Maths’.

1.2FD6 2.2FD7 3.2FD8 4a.2FDM 4b.2FD9 4c.2FDB 4d.2FDC 4e.2FDD

4f.2FDF 4g.2FDG 4h.2FDH 4i.2FDJ 4j.2FDK 4k.2FDN 4l.2FDP 4m.2FDQ

5a.2FDT 5b.2FDR 5c.2FDV 5d.2FDW 5e.2FDS

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4.5 Word problems EMA3D

To solve word problems we need to write a set of equations that represent the problem mathematically. The
solution of the equations is then the solution to the problem.

Problem solving strategy EMA3F

1.Read the whole question.

2.What are we asked to solve for?

3.Assign a variable to the unknown quantity, for example,x.

4.Translate the words into algebraic expressions by rewriting the given information in terms of the variable.

5.Set up an equation or system of equations to solve for the variable.

6.Solve the equation algebraically using substitution.

7.Check the solution.

VISIT:

The following video shows two examples of working with word problems.

See video:2FDXatwww.everythingmaths.co.za

Worked example 11: Solving word problems

QUESTION

A shop sells bicycles and tricycles. In total there are 7 cycles (cycles include both bicycles and tricycles) and

19 wheels. Determine how many of each there are, if a bicycle has two wheels and a tricycle has three wheels.

Chapter 4. Equations and inequalities 89