Elimination/Examples/Arbitrary Example 2

Example of Elimination

Consider the system of simultaneous linear equations:

\(\text {(1)}: \quad\)

\(\ds x + 3 y\)

\(=\)

\(\ds 7\)

\(\text {(2)}: \quad\)

\(\ds 2 x + y\)

\(=\)

\(\ds 9\)

This can be solved by putting $(1)$ in the form:

$x = 7 - 3 y$

from which we can substitute for $x$ in either $(2)$ to obtain:

$2 \paren {7 - 3 y} + y = 9$

from which it follows that $y = 1$ and $x = 4$.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): elimination
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): elimination