simultaneous equations

Practise simultaneous equations with an original VectorPaths question, worked explanation and related VCE Methods practice.

2 practice marks

Original practice question

Solve the simultaneous equations $\begin{cases} y = 1x^2 + -2x + 2 \\ y = 3x + 0 \end{cases}$.

Worked explanation

• Eliminate one variable

  \[\text{Solutions: } (\frac{5}{2} - \frac{\sqrt{17}}{2}, \frac{15}{2} - \frac{3 \sqrt{17}}{2}), \quad (\frac{\sqrt{17}}{2} + \frac{5}{2}, \frac{3 \sqrt{17}}{2} + \frac{15}{2})\]

• Write ordered pairs

  \[(\frac{5}{2} - \frac{\sqrt{17}}{2}, \frac{15}{2} - \frac{3 \sqrt{17}}{2}), \quad (\frac{\sqrt{17}}{2} + \frac{5}{2}, \frac{3 \sqrt{17}}{2} + \frac{15}{2})\]

\[(\frac{5}{2} - \frac{\sqrt{17}}{2}, \frac{15}{2} - \frac{3 \sqrt{17}}{2}), \quad (\frac{\sqrt{17}}{2} + \frac{5}{2}, \frac{3 \sqrt{17}}{2} + \frac{15}{2})\]

Original VectorPaths practice; not an official VCAA question or marking rubric.