All for One, One for All

Learning Focus

Choose and apply the best strategy (graphing, substitution, elimination) to solve systems and interpret answers in context.

Big idea

All system strategies find the same solution; the best choice depends on the form.

• Graphing: quick estimate, shows number of solutions.
• Substitution: best when a variable is isolated.
• Elimination: best when coefficients match or are opposites.
• Always check in both original equations.

Worked example

Solve $3x+2y=16$ and $5x-2y=8$.

The $y$-terms are opposites, so add: $8x=24\Rightarrow x=3$. Then $9+2y=16\Rightarrow y=3.5$.

Check: $5(3)-2(3.5)=15-7=8$.

Takeaways

• Match the method to the form of the equations.
• Every method gives the same ordered pair.
• Interpret the solution with units.