# How do solve the following linear system?:  5x+2y=2, x + y = 2 ?

$x = - \frac{2}{3}$ and $y = \frac{8}{3}$
Subtract y from both sides of the second equation and get $x = 2 - y$. Substitute this value of x in the first equation and get $5 \left(2 - y\right) + 2 y = 2$. Expanding the first term gives 10-5y+2y=2.Subtracting 10 from both sides and simplifying gives $- 3 y = - 8$. So, $y = \frac{8}{3}$. Substituting this value of y in $x = 2 - y$ gives $x = 2 - \left(\frac{8}{3}\right)$, so $x = \frac{6}{3} - \frac{8}{3}$ = $- \frac{2}{3}$.