Uvero — STEM Learning

Elimination in Simultaneous Equations

Elimination combines equations so one variable cancels, leaving a one-variable equation. Multiply an equation first when coefficients are not already opposites. A careful solution names the quantities, keeps place value or units visible, and explains why each operation fits.

Worked reasoning

Add the equations to eliminate $y$ : $2x=14$ .
$x=7$ .

Solve $x+y=10$ and $x-y=4$ . Find $x$ .

Which statement best captures the central mathematical idea in Elimination in Simultaneous Equations?

Multiply an equation first when coefficients are not already opposites.

A familiar-looking calculation may be used without checking place value, units, conditions or what the answer represents.

A memorised formula is valid even when its conditions are not met.

The diagram or notation replaces the need to justify each mathematical step.

When starting a problem about Elimination in Simultaneous Equations, which move is most reliable?

Represent the given information clearly and identify the operation or relationship required for elimination in simultaneous equations.

Round every value before identifying the mathematical structure.

Choose the longest available formula and substitute immediately.

Assume the desired conclusion and work backwards without checking equivalence.

Which statement is a misconception that must be rejected when working with Elimination in Simultaneous Equations?

A familiar-looking calculation may be used without checking place value, units, conditions or what the answer represents.

Multiply an equation first when coefficients are not already opposites.

Represent the given information clearly and identify the operation or relationship required for elimination in simultaneous equations.

Estimate first, then reverse the operation or use a second representation to check that the answer is reasonable.