Home > Graphing > Where two lines intersect

## Using the substitution method to find where two lines intersect

1. Rearrange one of the equations to make either x or y the subject
2. Substitute for either x or y depending on which one you made the subject
3. Solve the resulting equation
4. Substitute this value into one of the original equations to find the value of the other variable

Example

Find the coordinates where the lines $y=3x+5$ and $3x+2y=28$ intersect

Since the first equation already has y as the subject we will substitute this into the second

$\therefore 3x+2(3x+5)=28 \Rightarrow 9x+10=28 \Rightarrow x=2$

We now substitute this back into the first (on this occassion it is the easiest option)

and get $y=3 \times 2+5=11$

$\therefore$ the point of intersection in $(2,11)$