Elimination/Examples/Arbitrary Example 1

Example of Elimination

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

$\ds x + 3 y$

$=$

$\ds 7$

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

$\ds 2 x + y$

$=$

$\ds 9$

This can be solved by multiplying $(2)$ by $3$ and then subtracting $(1)$ from the resulting equation:

$\text {(3)}: \quad$

$\ds 6 x + 3 y$

$=$

$\ds 27$

$(2) \times 3$

$\ds \leadsto \ \ $

$\ds 5 x$

$=$

$\ds 20$

$(3) - (1)$

Hence $y$ has been eliminated, and we have:

$x = 4$

from which we can substitute for $x$ in either $(1)$ or $(2)$ and obtain $y = 1$.