Everything Maths Grade 10

Worked example 7: Simultaneous equations

QUESTION

Solve the following system of equations:

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

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

SOLUTION

Step 1: Use either equation to expressxin terms ofy

4 y+ 3x= 100

3 x= 100 4 y

x=

100  4 y

3

Step 2: Substitutexinto equation(2)and solve fory

4 y 19

(

100  4 y

3

)

= 12

12 y19 (100 4 y) = 36

12 y 1900 + 76y= 36

88 y= 1936

)y= 22

Step 3: Substituteyback into equation(1)and solve forx

x=

100 4 (22)

3

=

100 88

3

=

12

3

)x= 4

Step 4: Check the solution by substituting the answers back into both original equations

Step 5: Write the final answer

x= 4

y= 22

Chapter 4. Equations and inequalities 83