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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:
{y=2x+1x+y=7\begin{cases} y = 2x + 1 \\ x + y = 7 \end{cases}

Rearranging one equation first

Moderate

Problem

Solve the simultaneous equations:
{2x+y=10x−y=2\begin{cases} 2x + y = 10 \\ x - y = 2 \end{cases}

Solution involves a negative value

Challenging

Problem

Solve the simultaneous equations:
{y=2x+53x+y=0\begin{cases} y = 2x + 5 \\ 3x + y = 0 \end{cases}

Practise

Q1·Straightforward
Solve the simultaneous equations using substitution.
{y=x+2x+y=8\begin{cases} y = x + 2 \\ x + y = 8 \end{cases}

Enter your answer as (x, y).
Q2·Straightforward
Solve the simultaneous equations using substitution.
{y=2xx+y=9\begin{cases} y = 2x \\ x + y = 9 \end{cases}

Enter your answer as (x, y).
Q3·Straightforward
Solve the simultaneous equations using substitution.
{y=x−12x+y=11\begin{cases} y = x - 1 \\ 2x + y = 11 \end{cases}

Enter your answer as (x, y).
Q4·Straightforward
Solve the simultaneous equations using substitution.
{y=3x2x+y=10\begin{cases} y = 3x \\ 2x + y = 10 \end{cases}

Enter your answer as (x, y).
Q5·Moderate
Solve the simultaneous equations using substitution.
{x=y+2x+2y=8\begin{cases} x = y + 2 \\ x + 2y = 8 \end{cases}

Enter your answer as (x, y).
Q6·Moderate
Solve the simultaneous equations using substitution.
{y=x+12x−y=3\begin{cases} y = x + 1 \\ 2x - y = 3 \end{cases}

Enter your answer as (x, y).
Q7·Moderate
Solve the simultaneous equations using substitution.
{x=2y+1x+3y=16\begin{cases} x = 2y + 1 \\ x + 3y = 16 \end{cases}

Enter your answer as (x, y).
Q8·Moderate
Solve the simultaneous equations using substitution.
{y=4−x2x−y=2\begin{cases} y = 4 - x \\ 2x - y = 2 \end{cases}

Enter your answer as (x, y).
Q9·Challenging
Solve the simultaneous equations using substitution.
{y=2x−13x+2y=12\begin{cases} y = 2x - 1 \\ 3x + 2y = 12 \end{cases}

Enter your answer as (x, y).
Q10·Challenging
Solve the simultaneous equations using substitution.
{x=2y−12x−3y=1\begin{cases} x = 2y - 1 \\ 2x - 3y = 1 \end{cases}

Enter your answer as (x, y).
Q11·Challenging
Solve the simultaneous equations using substitution.
{y=2x+53x+y=0\begin{cases} y = 2x + 5 \\ 3x + y = 0 \end{cases}

Enter your answer as (x, y).
Q12·Challenging
Solve the simultaneous equations using substitution.
{x=3−2y4x+3y=2\begin{cases} x = 3 - 2y \\ 4x + 3y = 2 \end{cases}

Enter your answer as (x, y).