Question #f9676

Sep 2, 2017

You could use substitution (y = 1 - x) or linear systems.

Explanation:

Write the two equations as a linear system. Use algebraic properties to find the unknowns. A linear system can be solved as long as there are at least as many independent equations as there are variables.
$2 x = 5 y$
$x + y = 1$ First, get all of the variables on one side:
$2 x - 5 y = 0$
$x + y = 1$; Now multiply the second equation by 5d and add it to the first one:
$2 x - 5 y = 0$
$5 x + 5 y = 5$

$7 x = 5$; $x = \frac{5}{7}$; Substitute this value back into the first equation to find the 'y'.
$2 \left(\frac{5}{7}\right) = 5 y$; $\left(\frac{2}{5}\right) \left(\frac{5}{7}\right) = y$; $y = \frac{2}{7}$
CHECK by putting both values into the second equation:

$x + y = 1$ ; $\frac{5}{7} + \frac{2}{7} = 1$ ; $1 = 1$ CORRECT!