Mathematics » Equations and Inequalities » Simultaneous Equations Continued

# Solving Graphically II

## Solving Graphically

• Make $$y$$ the subject of each equation.

• Draw the graph of each equation on the same system of axes.

• The final solutions to the system of equations are the coordinates of the points where the two graphs intersect.

## Example

### Question

Solve graphically for $$x$$ and $$y$$: \begin{align*} y + x^2 &= 1 \qquad \ldots (1) \\ y – x + 5 &= 0 \qquad \ldots (2) \end{align*}

### Make $$y$$ the subject of both equations

For the first equation we have

\begin{align*} y + x^2 &= 1 \\ y &= – x^2 + 1 \end{align*}

and for the second equation

\begin{align*} y – x + 5 &= 0 \\ y &= x – 5 \end{align*}

### Determine where the two graphs intersect

From the diagram we see that the graphs intersect at $$(-3;-8)$$ and $$(2;-3)$$.

### Check that the two points satisfy both original equations

The solutions to the system of simultaneous equations are $$(-3;-8)$$ and $$(2;-3)$$.