Everything Maths Grade 10

Worked example 10: Simultaneous equations

QUESTION

Solve the following system of simultaneous equations graphically:

4 y+ 3x= 100 : : :(1)

4 y 19 x= 12 : : :(2)

SOLUTION

Step 1: Write both equations in formy=mx+c

4 y+ 3x= 100

4 y= 100 3 x

y=

3

4

x+ 25

4 y 19 x= 12

4 y= 19x+ 12

y=

19

4

x+ 3

Step 2: Sketch the graphs on the same set of axes

 8  6  4  2 2 4 6 8

5

10

15

20

25

30

y= 43 x+ 25

y=^194 x+ 3

(4; 22)

x

y

Step 3: Find the coordinates of the point of intersection

The two graphs intersect at(4; 22)

Step 4: Write the final answer

x= 4

y= 22

Chapter 4. Equations and inequalities 87