Everything Maths Grade 10

Solving by substitution EMA39

• Use the simplest of the two given equations to express one of the variables in terms of the other.


• Substitute into the second equation. By doing this we reduce the number of equations and the number
  of variables by one.


• We now have one equation with one unknown variable which can be solved.


• Use the solution to substitute back into the first equation to find the value of the other unknown variable.

VISIT:

The following video shows how to solve simultaneous equations using substitution.

See video:2FD5atwww.everythingmaths.co.za

Worked example 6: Simultaneous equations

QUESTION

Solve forxandy:

xy= 1 : : :(1)

3 =y 2 x : : :(2)

SOLUTION

Step 1: Use equation(1)to expressxin terms ofy

x=y+ 1

Step 2: Substitutexinto equation(2)and solve fory

3 =y2 (y+ 1)

3 =y 2 y 2

5 =y

)y= 5

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

x= (5) + 1

)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= 5

82 4.4. Solving simultaneous equations