# How do you solve the system of equations 50x + 40= y and 30x + 45= y?

Apr 16, 2018

$x = 0.25 , y = 52.5$

#### Explanation:

$\therefore 50 x + 40 = y - - - - - - \left(1\right)$

$\therefore 30 x + 45 = y - - - - - - \left(2\right)$

$\therefore \left(1\right) - \left(2\right)$

$\therefore 20 x - 5 = 0$

$\therefore 20 x = 5$

$\therefore x = {\cancel{5}}^{1} / {\cancel{20}}^{4}$

$\therefore x = \frac{1}{4}$ or $0.25$

substitute x=0.25 in (1)

$\therefore 50 \left(0.25\right) + 40 = y$

$\therefore 12.5 + 40 = y$

$\therefore y = 52.5$

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check:-

substitute $x = 0.25$and $y = 52.5$ in$\left(2\right)$

$\therefore 30 \left(0.25\right) + 45 = 52.5$

$\therefore 7.5 + 45 = 52.5$

$\therefore 52.5 = 52.5$