Substitution method
Solve simultaneous equations by substituting one equation into the other. Works best when one equation is already solved for a variable.
Worked examples
One equation already solved for y
Straightforward
Problem
Solve the simultaneous equations:
1
The first equation is already solved for . Substitute it into the second equation.
2
Expand and simplify.
3
Solve for .
4
Substitute back into the first equation to find .
5
Check by substituting into both original equations.
Equation 1: ✓
Equation 2: ✓
Equation 2: ✓
Answer
,
Rearranging one equation first
Moderate
Problem
Solve the simultaneous equations:
1
Neither equation is solved for a single variable. Rearrange the second equation to isolate .
2
Substitute this expression for into the first equation.
3
Expand and simplify.
4
Substitute back into .
5
Check in both original equations.
Equation 1: ✓
Equation 2: ✓
Equation 2: ✓
Answer
,
Solution involves a negative value
Challenging
Problem
Solve the simultaneous equations:
1
Substitute into the second equation.
2
Simplify and solve for .
3
Substitute into .
4
Check in both original equations.
Equation 1: ✓
Equation 2: ✓
Equation 2: ✓
Answer
,
Practise
Q1·Straightforward
Solve the simultaneous equations using substitution.
Enter your answer as (x, y).
Enter your answer as (x, y).
Explanation
Substitute into :
Substitute into :
Check: ✓
Solution: ,
Substitute into :
Check: ✓
Solution: ,
Q2·Straightforward
Solve the simultaneous equations using substitution.
Enter your answer as (x, y).
Enter your answer as (x, y).
Explanation
Substitute into :
Substitute into :
Check: ✓
Solution: ,
Substitute into :
Check: ✓
Solution: ,
Q3·Straightforward
Solve the simultaneous equations using substitution.
Enter your answer as (x, y).
Enter your answer as (x, y).
Explanation
Substitute into :
Substitute into :
Check: ✓
Solution: ,
Substitute into :
Check: ✓
Solution: ,
Q4·Straightforward
Solve the simultaneous equations using substitution.
Enter your answer as (x, y).
Enter your answer as (x, y).
Explanation
Substitute into :
Substitute into :
Check: ✓
Solution: ,
Substitute into :
Check: ✓
Solution: ,
Q5·Moderate
Solve the simultaneous equations using substitution.
Enter your answer as (x, y).
Enter your answer as (x, y).
Explanation
Substitute into :
Substitute into :
Check: ✓
Solution: ,
Substitute into :
Check: ✓
Solution: ,
Q6·Moderate
Solve the simultaneous equations using substitution.
Enter your answer as (x, y).
Enter your answer as (x, y).
Explanation
Substitute into :
Substitute into :
Check: ✓
Solution: ,
Substitute into :
Check: ✓
Solution: ,
Q7·Moderate
Solve the simultaneous equations using substitution.
Enter your answer as (x, y).
Enter your answer as (x, y).
Explanation
Substitute into :
Substitute into :
Check: ✓
Solution: ,
Substitute into :
Check: ✓
Solution: ,
Q8·Moderate
Solve the simultaneous equations using substitution.
Enter your answer as (x, y).
Enter your answer as (x, y).
Explanation
Substitute into :
Substitute into :
Check: ✓
Solution: ,
Substitute into :
Check: ✓
Solution: ,
Q9·Challenging
Solve the simultaneous equations using substitution.
Enter your answer as (x, y).
Enter your answer as (x, y).
Explanation
Substitute into :
Substitute into :
Check: ✓
Solution: ,
Substitute into :
Check: ✓
Solution: ,
Q10·Challenging
Solve the simultaneous equations using substitution.
Enter your answer as (x, y).
Enter your answer as (x, y).
Explanation
Substitute into :
Substitute into :
Check: ✓
Solution: ,
Substitute into :
Check: ✓
Solution: ,
Q11·Challenging
Solve the simultaneous equations using substitution.
Enter your answer as (x, y).
Enter your answer as (x, y).
Explanation
Substitute into :
Substitute into :
Check: ✓
Solution: ,
Substitute into :
Check: ✓
Solution: ,
Q12·Challenging
Solve the simultaneous equations using substitution.
Enter your answer as (x, y).
Enter your answer as (x, y).
Explanation
Substitute into :
Substitute into :
Check: ✓
Solution: ,
Substitute into :
Check: ✓
Solution: ,
Open Math
Substitution method
Algebra · MA5-EQU-P-01
Name:
Date:
Q1Straightforward
Solve the simultaneous equations using substitution.
Enter your answer as (x, y).
Enter your answer as (x, y).
Q2Straightforward
Solve the simultaneous equations using substitution.
Enter your answer as (x, y).
Enter your answer as (x, y).
Q3Straightforward
Solve the simultaneous equations using substitution.
Enter your answer as (x, y).
Enter your answer as (x, y).
Q4Straightforward
Solve the simultaneous equations using substitution.
Enter your answer as (x, y).
Enter your answer as (x, y).
Q5Moderate
Solve the simultaneous equations using substitution.
Enter your answer as (x, y).
Enter your answer as (x, y).
Q6Moderate
Solve the simultaneous equations using substitution.
Enter your answer as (x, y).
Enter your answer as (x, y).
Q7Moderate
Solve the simultaneous equations using substitution.
Enter your answer as (x, y).
Enter your answer as (x, y).
Q8Moderate
Solve the simultaneous equations using substitution.
Enter your answer as (x, y).
Enter your answer as (x, y).
Q9Challenging
Solve the simultaneous equations using substitution.
Enter your answer as (x, y).
Enter your answer as (x, y).
Q10Challenging
Solve the simultaneous equations using substitution.
Enter your answer as (x, y).
Enter your answer as (x, y).
Q11Challenging
Solve the simultaneous equations using substitution.
Enter your answer as (x, y).
Enter your answer as (x, y).
Q12Challenging
Solve the simultaneous equations using substitution.
Enter your answer as (x, y).
Enter your answer as (x, y).
Worked solutions and answers at openmath.au/year-9/simultaneous-equations/substitution-method