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.



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*}

Draw the straight line graph and parabola on the same system of axes


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

Write the final answer

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

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