Solving Simultaneous Equations Graphically
Example
Solve the following pair of equations by drawing graphs:
\[
x + y = 6
\]
\[
x - y = -4
\]
Solution
- Rearrange equations into the form \(y = mx + c\)
\[
y = 6 - x
\]
\[
y = x + 4
\]
- Take the first equation.
Pick 3 sensible values for \(x\), then solve for \(y\). Substitute each value of \(x\) into the equation.
For example, when \(x = -2\): \[ y = 6 - (-2) = 8 \]
Plot the points \((-2,8)\), \((0,6)\), \((6,0)\) and join with a straight line.
Graph of \(y = 6 - x\)
- Repeat for the other equation.
Plot the points \((-4,0)\), \((0,4)\), \((4,8)\) and join with a straight line.
Graph of \(y = x + 4\)
- Read off the intersection point.
The lines intersect at \((1,5)\). So \(x = 1\), \(y = 5\).
Check
\[
x + y = 6 \quad \Rightarrow \quad 1 + 5 = 6
\]
\[
x - y = -4 \quad \Rightarrow \quad 1 - 5 = -4
\]
The solution is the point of intersection: \((1,5)\)
