Everything Maths Grade 10

Worked example 9: Simultaneous equations

QUESTION

Solve the following system of equations:

2 a 3 b= 5 : : :(1)

3 a 2 b= 20 : : :(2)

SOLUTION

Step 1: Make the coefficients of one of the variables the same in both equations

By multiplying equation(1)by 3 and equation(2)by 2, both coefficients ofawill be 6.

6 a 9 b = 15

 (6a 4 b = 40)

0  5 b =  25

(When subtracting two equations, be careful of the signs.)

Step 2: Simplify and solve forb

b=

25

5

)b= 5

Step 3: Substitute value ofbback into either original equation and solve fora

2 a3 (5) = 5

2 a15 = 5

2 a= 20

)a= 10

Step 4: Check that the solutiona= 10andb= 5satisfies both original equations

Step 5: Write the final answer

a= 10

b= 5

Chapter 4. Equations and inequalities 85